Exhibit 4.1

INMUNE BIO INC.

AMENDMENT NO. 5 TO RIGHTS AGREEMENT

This Amendment No. 5 (this “Amendment”), dated as of December 5, 2025, to the Rights Agreement, dated December 30, 2020, as amended on December 20, 2021, December 9, 2022, December 14, 2023 and December 6, 2024 (the “Rights Agreement”), between INmune Bio Inc., a Nevada corporation (the “Company”), and VStock Transfer LLC, as rights agent (the “Rights Agent”).

WHEREAS, the Company and the Rights Agent have executed and entered into the Rights Agreement;

WHEREAS, Section 27 of the Rights Agreement provides, the Company, by action of the Board, may from time to time and in its sole and absolute discretion, and the Rights Agent shall if the Company so directs, supplement or amend the Rights Agreement in any respect without the approval of any holders of Rights, including, without limitation to shorten or lengthen any time period provided in the Rights Agreement;

WHEREAS, to the knowledge of the Company, no Person has become an Acquiring Person;

WHEREAS, the Board of Directors of the Company has deemed it advisable and in the best interests of the Company and its stockholders to amend certain provisions of the Rights Agreement as set forth herein; and

WHEREAS, pursuant to and in accordance with Section 27 of the Rights Agreement, the Company desires to amend the Rights Agreement as set forth below.

NOW THEREFORE, in consideration of the foregoing and the mutual agreements set forth in the Rights Agreement and this Amendment, the parties hereto hereby agree as follows:

1. Section 7(a) of the Rights Agreement is hereby amended and restated as follows:

“(a) Subject to Section 7(e) hereof or as otherwise provided in this Agreement, at any time after the Distribution Date the registered holder of any Rights Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein including, without limitation, the restrictions on exercisability set forth in Section 9(c), Section 11(a)(iii), and Section 23(a) hereof) in whole or in part upon surrender of the Rights Certificate, with the form of election to purchase and the certificate contained therein properly completed and duly executed, to the Rights Agent at the office or offices of the Rights Agent designated for such purpose, accompanied by a signature guarantee and such other documentation as the Rights Agent may reasonably request, together with payment of the aggregate Purchase Price with respect to the total number of one one-thousandths of a Preferred Share (or, following the occurrence of a Triggering Event, Common Shares, other securities, cash or other assets, as the case may be) as to which such surrendered Rights are then exercisable, at or prior to the earliest of (i) the Close of Business on December 31, 2026 (the “Final Expiration Date”), (ii) the time at which the Rights are redeemed as provided in Section 23 hereof (the “Redemption Date”), and (iii) the time at which the Rights are exchanged in full as provided in Section 24 hereof (the earliest of (i), (ii), and (iii) being herein referred to as the “Expiration Date”). From and after the Final Expiration Date, this Agreement shall automatically renew for successive one-year terms on each anniversary of the Final Expiration Date (each, an “Extended Term”), unless, prior to the commencement of any such Extended Term, the Board determines not to extend this Agreement, in which case the Agreement shall expire at the end of the then-current term. The Company shall provide the Rights Agent with written notice of any such determination by the Board. Except for those provisions herein that expressly survive the termination of this Agreement, this Agreement shall terminate at such time as the Rights are no longer exercisable hereunder.”

3.  Exhibit B. Exhibit B to the Rights Agreement is hereby amended by deleting all references therein to “December 30, 2025” and inserting “December 31, 2026 (as such date may be automatically extended in accordance with Section 7(a) of the Rights Agreement)” in place thereof.

4. Exhibit C. Exhibit C to the Rights Agreement is hereby amended by deleting the reference therein to “December 30, 2025” and inserting “December 31, 2026 (as such date may be automatically extended in accordance with Section 7(a) of the Rights Agreement)” in place thereof.

5. Full Force and Effect. Except as expressly amended hereby, the Rights Agreement shall continue in full force and effect in accordance with the provisions thereof.

6. Governing Law.  This Amendment shall be deemed to be a contract made under the laws of the State of Nevada and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State; provided, that all provisions regarding the rights, duties, liabilities and obligations of the Rights Agent shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within the State of New York.

7. Counterparts; Facsimiles and PDFs; Effectiveness. This Amendment may be executed in any number of counterparts and each of such counterparts will for all purposes be deemed to be an original, and all such counterparts will together constitute one and the same instrument, it being understood that all parties need not sign the same counterpart. A signature to this Amendment executed or transmitted electronically (including by facsimile and a portable document format signature) will have the same authority, effect and enforceability as an original signature. No party hereto may raise the use of such electronic execution or transmission to deliver a signature, or the fact that any signature or agreement or instrument was transmitted or communicated through such electronic transmission, as a defense to the formation of a contract, and each party forever waives any such defense, except to the extent such defense relates to lack of authenticity.  This Amendment shall be effective as of the date hereof.

8. Descriptive Headings. Descriptive headings of the several sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions of this Amendment.

9. Rights Agreement as Amended. From and after the date hereof, any reference to the Rights Agreement shall mean the Rights Agreement as amended hereby.

10. Severability. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the day and year first above written.