Exhibit 10.4

NUWELLIS, INC.

January 29, 2026

Holder of Common Stock Purchase Warrants issued on November 6, 2024 and June 10, 2025

Re:       Inducement Offer to Exercise Common Stock Purchase Warrants

Dear Holder:

Nuwellis, Inc. (the “Company”) is pleased to offer to you the opportunity to receive new warrants to purchase shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”), in consideration for exercising by you for cash all of (i) the Series I Common Stock Purchase Warrants issued on November 6, 2024 (the “Series I Warrants”), (ii) the Series II Common Stock Purchase Warrants issued on November 6, 2024 (the “Series II Warrants”), (iii) the Series A Common Stock Purchase Warrants issued on June 10, 2025 (the “Series A Warrants”), and (iv) the Series B Common Stock Purchase Warrants issued on June 10, 2025 (the “Series B Warrants”, together with the Series I Warrants, the Series II Warrants and the Series A Warrants, the “Existing Warrants”) set forth on the signature page hereto currently held by you (the “Holder”) to a reduced exercise price of $2.84 per share (the “Reduced Exercise Price”) and the payment of $0.125 per New Warrant (the “New Warrant Consideration”).  The shares underlying the Existing Warrants (the “Warrant Shares”) have been registered pursuant to the registration statements on Form S-1 (File No. 333- 283283) and Form S-1 (File No. 333-287663) (collectively, the “Registration Statement”). The Registration Statement is currently effective and, upon exercise of the Existing Warrants pursuant to this letter agreement (this “Agreement”), will be effective for the issuance or sale, as the case may be, of the Warrant Shares. Capitalized terms not otherwise defined herein shall have the meanings set forth in the applicable Existing Warrant (or the securities purchase agreements executed in connection with the applicable Existing Warrant).

In consideration for exercising in full for cash all of the Existing Warrants held by you and set forth on the signature page hereto (the “Warrant Exercise”) at the Reduced Exercise Price on or before the Execution Time (as defined below) and the payment by the Holder on the Closing Date of the New Warrant Consideration, the Company hereby offers to sell and issue you or your designee, a new Common Stock Purchase Warrant (the “New Warrants”) pursuant to Section 4(a)(2) of the Securities Act of 1933, as amended (“Securities Act”) to purchase up to such number of shares of Common Stock (“New Warrant Shares”) equal to 200% of the number of Warrant Shares issued pursuant to the Warrant Exercise of the Existing Warrants hereunder, which New Warrants shall be substantially in the form of Annex B attached hereto. The New Warrant will be immediately exercisable from the date of issuance, will have a term of exercise of five (5) years from the effective date of the Resale Registration Statement, and an exercise price per share equal to $2.84.

The original warrant certificates for the New Warrants will be delivered within two (2) Business Days following each Warrant Exercise pursuant to this Agreement. Notwithstanding anything herein to the contrary, in the event the Warrant Exercise would otherwise cause the Holder to exceed the beneficial ownership limitations (“Beneficial Ownership Limitation”) set forth in Section 2(e) of each of the Existing Warrants, the Company shall only issue such number of Warrant Shares to the Holder that would not cause the Holder to exceed the maximum number of Warrant Shares permitted thereunder with the balance to be held in abeyance until notice from the Holder that the balance (or portion thereof) may be issued in compliance with such limitations, which abeyance shall be evidenced through the Existing Warrants which shall be deemed prepaid thereafter, and exercised pursuant to a Notice of Exercise in the applicable Existing Warrant (provided no additional exercise shall be payable).

Expressly subject to the paragraph immediately following this paragraph below, Holder may accept this offer by signing this letter below, with such acceptance constituting Holder's exercise in full of the Existing Warrants for an aggregate exercise price set forth on the Holder’s signature page hereto (the “Warrants Exercise Price”) on or before 4:00 p.m. Eastern Time on January 29, 2026 (the “Execution Time”).

Additionally, the Company agrees to the representations, warranties and covenants set forth on Annex A attached hereto.  Holder represents and warrants (i) that it is an “accredited investor” as defined in Rule 501 of the Securities Act, and (ii) that it is acquiring the New Warrants as principal for its own account and has no direct or indirect arrangement or understandings with any other persons to distribute or regarding the distribution of the New Warrants or the New Warrant Shares (this representation is not limiting Holder’s right to sell the New Warrant Shares pursuant to an effective registration statement under the Securities Act or otherwise in compliance with applicable federal and state securities laws). Holder agrees that the New Warrants will contain restrictive legends when issued, and neither the New Warrants nor the shares of Common Stock issuable upon exercise of the New Warrants will be registered under the Securities Act upon issuance.

The Holder understands that the New Warrants and the shares of Common Stock underlying the New Warrants are not, and may never be, registered under the Securities Act, or the securities laws of any state and, accordingly, each certificate, if any, representing such securities shall bear a legend substantially similar to the following:

“NEITHER THIS SECURITY NOR THE SECURITIES FOR WHICH THIS SECURITY IS EXERCISABLE HAVE BEEN REGISTERED WITH THE SECURITIES AND EXCHANGE COMMISSION OR THE SECURITIES COMMISSION OF ANY STATE IN RELIANCE UPON AN EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “SECURITIES ACT”), AND, ACCORDINGLY, MAY NOT BE OFFERED OR SOLD EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR PURSUANT TO AN AVAILABLE EXEMPTION FROM, OR IN A TRANSACTION NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT AND IN ACCORDANCE WITH APPLICABLE STATE SECURITIES LAWS. THIS SECURITY AND THE SECURITIES ISSUABLE UPON EXERCISE OF THIS SECURITY MAY BE PLEDGED IN CONNECTION WITH A BONA FIDE MARGIN ACCOUNT OR OTHER LOAN SECURED BY SUCH SECURITIES.”

Book-entry statements evidencing shares of Common Stock underlying the New Warrants shall not contain any legend (including the legend set forth above), (i) while a registration statement covering the resale of such Common Stock is effective under the Securities Act, (ii) following any sale of such Common Stock pursuant to Rule 144 under the Securities Act, (iii) if such Common Stock is eligible for sale under Rule 144, without the requirement for the Company to be in compliance with the current public information required under Rule 144 as to such Common Stock and without volume or manner-of-sale restrictions, (iv) if such Common Stock may be sold under Rule 144 and the Company is then in compliance with the current public information required under Rule 144 as to such Common Stock, or (v) if such legend is not required under applicable requirements of the Securities Act (including judicial interpretations and pronouncements issued by the staff of the Securities and Exchange Commission (the “Commission”) and the earliest of clauses (i) through (v), (the “Delegend Date”)). Upon receipt of a representation letter or other documentation from the Holder that the Company may reasonably request, the Company shall cause its counsel to issue a legal opinion to the transfer agent promptly after the Delegend Date if required by the Company and/or the transfer agent to effect the removal of the legend hereunder, which opinion shall be in form and substance reasonably acceptable to the Holder. If such Common Stock may be sold under Rule 144 without the requirement for the Company to be in compliance with the current public information required under Rule 144 or if such legend is not otherwise required under applicable requirements of the Securities Act (including judicial interpretations and pronouncements issued by the staff of the Commission) then such Common Stock shall be issued free of all legends. The Company agrees that following the Delegend Date or at such time as such legend is no longer required, it will, no later than one (1) Trading Day following the delivery by the Holder to the Company or the transfer agent of a book-entry statement evidencing the Common Stock underlying the New Warrants issued with a restrictive legend and a representation letter from the Holder that the Company may reasonably request  (such Trading Day, the “Legend Removal Date”), deliver or cause to be delivered to the Holder a book-entry statement evidencing such shares that is free from all restrictive and other legends or, at the request of the Holder shall credit the account of the Holder’s prime broker with the Depository Trust Company System as directed by the Holder.

In addition to the Holder’s other available remedies, the Company shall pay to a Holder, in cash, (i) as partial liquidated damages and not as a penalty, for each $1,000 of Warrant Shares (based on the VWAP of the Common Stock on the date such Warrant Shares are submitted to the Transfer Agent) delivered for removal of the restrictive legend, $10 per Trading Day (increasing to $20 per Trading Day five (5) Trading Days after such damages have begun to accrue) for each Trading Day after the Legend Removal Date until such book-entry statement is delivered without a legend and (ii) if the Company fails to (a) issue and deliver (or cause to be delivered) to the Holder by the Legend Removal Date a book-entry statement evidencing the Warrant Shares so delivered to the Company by the Holder that is free from all restrictive and other legends and (b) if after the Legend Removal Date the Holder purchases (in an open market transaction or otherwise) shares of Common Stock to deliver in satisfaction of a sale by the Holder of all or any portion of the number of shares of Common Stock, or a sale of a number of shares of Common Stock equal to all or any portion of the number of shares of Common Stock that the Holder anticipated receiving from the Company without any restrictive legend, then, an amount equal to the excess of the Holder’s total purchase price (including brokerage commissions and other out-of-pocket expenses, if any) for the shares of Common Stock so purchased (including brokerage commissions and other out-of-pocket expenses, if any) over the product of (A) such number of Warrant Shares that the Company was required to deliver to the Holder by the Legend Removal Date multiplied by (B) the lowest closing sale price of the Common Stock on any Trading Day during the period commencing on the date of the delivery by the Holder to the Company of the applicable Warrant Shares (as the case may be) and ending on the date of such delivery and payment under this clause (ii).

If this offer is accepted and the transaction documents are executed on or before the Execution Time, then as promptly as possible following the Execution Time, but in any event no later than 9:00 a.m. Eastern Time on the date immediately following the date hereof, the Company shall issue a press release disclosing all material terms of the transactions contemplated hereunder and shall file a Current Report on Form 8-K with the Securities and Exchange Commission disclosing all material terms of the transactions contemplated hereunder, including the filing of this Agreement as an exhibit thereto within the time required by the Exchange Act From and after the issuance of such press release, the Company represents to you that it shall have publicly disclosed all material, non-public information delivered to you by the Company, or any of their respective officers, directors, employees or agents in connection with the transactions contemplated hereunder.  In addition, effective upon the issuance of such press release, the Company acknowledges and agrees that any and all confidentiality or similar obligations under any agreement, whether written or oral, between the Company, any of its subsidiaries or any of their respective officers, directors, agents, employees or Affiliates on the one hand, and you and your Affiliates on the other hand, shall terminate.  The Company represents, warrants and covenants that, upon acceptance of this offer and entering into this Agreement, the shares underlying the Existing Warrants shall be issued free of any legends or restrictions on resale by Holder and all of the Warrant Shares shall be delivered electronically through the Depository Trust Company within one (1) Business Day following the date hereof (or, with respect to Warrant Shares that would otherwise be in excess of the Beneficial Ownership Limitation, within one (1) Business Day of the date the Company is notified by Holder that its ownership is less than the applicable Beneficial Ownership Limitation), provided the payment of the Warrants Exercise Price is received by the Company prior to issuing such Warrant Shares.  The terms of the Existing Warrants, including but not limited to the obligations to deliver the Warrant Shares, shall otherwise remain in effect as if the acceptance of this offer were a formal Notice of Exercise (including but not limited to any liquidated damages and compensation in the event of late delivery of the Warrant Shares).

The Company agrees that within fifteen (15) calendar days of the date hereof, the Company shall file a registration statement on Form S-3 (or other appropriate form if the Company is not then eligible to register securities on Form S-3) (the “Resale Registration Statement”) providing for the resale by the Holders of the New Warrant Shares issued and issuable upon exercise of the New Warrants.  The Company shall use commercially reasonable efforts to cause such registration to become effective within forty-five (45) days (or sixty (60) days if the Commission notifies the Company that it will “review” the registration statement) following the initial filing of such registration statement and to keep such registration statement effective at all times until the earlier of (i) the time that no Holder owns any New Warrants or New Warrant Shares issuable upon exercise thereof or (ii) the Delegend Date.

The Company acknowledges and agrees that the obligations of the Holders under this Agreement are several and not joint with the obligations of any other Holder or any other holders of warrants to purchase Common Stock or other warrants of the Company (each, an “Other Holder”) under any other agreement related to the exercise of such common stock purchase warrants (“Other Warrant Exercise Agreement”), and the Holder shall not be responsible in any way for the performance of the obligations of any Other Holder or under any such Other Warrant Exercise Agreement.  Nothing contained in this Agreement, and no action taken by the Holders pursuant hereto, shall be deemed to constitute the Holder and the Other Holders as a partnership, an association, a joint venture or any other kind of entity, or create a presumption that the Holder and the Other Holders are in any way acting in concert or as a group with respect to such obligations or the transactions contemplated by this Agreement and the Company acknowledges that the Holder and the Other Holders are not acting in concert or as a group with respect to such obligations or the transactions contemplated by this Agreement or any Other Warrant Exercise Agreement.  The Company and the Holder confirm that the Holder has independently participated in the negotiation of the transactions contemplated hereby with the advice of its own counsel and advisors.  The Holder shall be entitled to independently protect and enforce its rights, including, without limitation, the rights arising out of this Agreement, and it shall not be necessary for any Other Holder to be joined as an additional party in any proceeding for such purpose.

***************

To accept this offer, Holder must counter execute this Agreement and return the fully executed Agreement to the Company at e-mail: John.Erb@nuwellis.com, attention: John Erb, on or before the Execution Time.

Please do not hesitate to call me if you have any questions.

	Sincerely yours,
	NUWELLIS, INC.
	By:
	Name:
	Title:

[Holder Signature Page Follows]

Accepted and Agreed to:

Name of Holder: ________________________________________________________

Signature of Authorized Signatory of Holder: _________________________________

Name of Authorized Signatory: _______________________________________________

Title of Authorized Signatory: ________________________________________________

Total Series I Warrant Shares being exercised contemporaneously with signing this Agreement: _________________

Total Series II Warrant Shares being exercised contemporaneously with signing this Agreement: _________________

Total Series A Warrant Shares being exercised contemporaneously with signing this Agreement: _________________

Total Series B Warrant Shares being exercised contemporaneously with signing this Agreement: _________________

Aggregate Exercise Price being exercised contemporaneously with signing this Agreement: ____

_________________

Aggregate New Warrant Consideration: $__________ ($0.125 per Existing Warrant)

New Warrants (200% of total Existing Warrants being exercised): ___________

New Warrants Beneficial Ownership Blocker: ☐ 4.99% or ☐ 9.99%

DTC Instructions:

Representations, Warranties and Covenants of the Company.  The Company hereby makes the following representations and warranties to the Holder:

(a)       Registration Statement. The existing Warrant Shares are registered for issuance on the Registration Statement and the Company knows of no reason why such Registration Statement shall not remain effective for the foreseeable future. The Company shall use commercially reasonable efforts to keep the Registration Statement effective and available for use by the Holder until all existing Warrant Shares underlying the Existing Warrants are sold by the Holder.

 

(b)        Authorization; Enforcement.  The Company has the requisite corporate power and authority to enter into and to consummate the transactions contemplated by this Agreement and otherwise to carry out its obligations hereunder and thereunder.  The execution and delivery of this Agreement by the Company and the consummation by the Company of the transactions contemplated hereby have been duly authorized by all necessary action on the part of the Company and no further action is required by the Company, its board of directors or its stockholders in connection therewith.  This Agreement has been duly executed by the Company and, when delivered in accordance with the terms hereof, will constitute the valid and binding obligation of the Company enforceable against the Company in accordance with its terms, except (i) as limited by general equitable principles and applicable bankruptcy, insolvency, reorganization, moratorium and other laws of general application affecting enforcement of creditors’ rights generally, (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies and (iii) insofar as indemnification and contribution provisions may be limited by applicable law.

 

(c)         No Conflicts.  The execution, delivery and performance of this Agreement by the Company and the consummation by the Company of the transactions contemplated hereby do not and will not: (i) conflict with or violate any provision of the Company’s certificate of incorporation, as amended, bylaws, or other organizational or charter documents; or (ii) conflict with, or constitute a default (or an event that with notice or lapse of time or both would become a default) under, result in the creation of any liens, claims, security interests, other encumbrances or defects upon any of the properties or assets of the Company in connection with, or give to others any rights of termination, amendment, acceleration or cancellation (with or without notice, lapse of time or both) of, any material agreement, credit facility, debt or other material instrument (evidencing Company debt or otherwise) or other material understanding to which such Company is a party or by which any property or asset of the Company is bound or affected; or (iii) conflict with or result in a violation of any law, rule, regulation, order, judgment, injunction, decree or other restriction of any court or governmental authority to which the Company is subject (including federal and state securities laws and regulations), or by which any property or asset of the Company is bound or affected, except, in the case of each of clauses (ii) and (iii), such as could not have or reasonably be expected to result in a material adverse effect upon the business, prospects, properties, operations, condition (financial or otherwise) or results of operations of the Company, taken as a whole, or in its ability to perform its obligations under this Agreement.

 

(d)         Nasdaq Corporate Governance.  The transactions contemplated under this Agreement, comply with all rules of the Nasdaq Capital Market.

 

(e)         Issuance of the New Warrant. The issuance of the New Warrants is duly authorized and, and when executed and delivered by the Company, shall constitute a valid, legal and binding obligation of the Company, enforceable in accordance with their terms, except as such enforceability may be limited by bankruptcy, insolvency, reorganization or similar laws affecting the rights of creditors generally and subject to general principles of equity, and the New Warrant Shares, when issued in accordance with the terms of the New Warrants, will be validly issued, fully paid and nonassessable, free and clear of all liens imposed by the Company. The Company has reserved from its duly authorized capital stock a number of shares of Common Stock for issuance of the New Warrant Shares in full.

 

(f)          Listing of Common Stock. The Company shall apply to list or quote all of the New Warrant Shares on the Nasdaq Capital Market and promptly secure the listing of all of the New Warrant Shares on the Nasdaq Capital Market.

 

(g)         Subsequent Equity Sales.  From the date hereof until forty-five (45) days after the effective date of the Reseale Registration Statement, neither the Company nor any subsidiary shall (i) issue, enter into any agreement to issue or announce the issuance or proposed issuance of any shares of Common Stock or Common Stock Equivalents or (ii) file any registration statement or any amendment or supplement thereto, in each case other than the registration statement registering the New Warrant Shares.  Notwithstanding the foregoing, this Section (g) shall not apply in respect of an Exempt Issuance (as defined in the certain Securities Purchase Agreement, dated as of January 29, 2026 (the ”Purchase Agreement”), by and between the Company and the signatory therein), except that no Variable Rate Transaction (as defined in the Purchase Agreement) shall be an Exempt Issuance.

 

(h)        Variable Rate Transactions. From the date hereof until three (3)  months after the effective date of the Resale Registration Statement, the Company shall be prohibited from effecting or entering into an agreement to effect any issuance by the Company or any of its subsidiaries of common stock or common stock equivalents (or a combination of units thereof) involving a Variable Rate Transaction; provided, however, that, the entry into and/or issuance of shares of common stock in an “at the market” offering with Ladenburg Thalmann & Co. Inc. as sales agent after forty-five (45) days after the closing date shall not be deemed a Variable Rate Transaction.  Any Holder shall be entitled to obtain injunctive relief against the Company to preclude any such issuance, which remedy shall be in addition to any right to collect damages.

 

(i)         Current Issued and Outstanding.  As of the date hereof, the Company represents and warrants it has 1,686,892 shares of common stock issued and outstanding.