Exhibit 99.4

Lynx1 Capital Management LP

D81 Calle C

Suite 301, PMB 1202

Dorado, Puerto Rico 00646-2051

(929) 888-7476

December 2, 2025

The Board of Directors of Neuphoria Therapeutics Inc.

100 Summit Drive

Burlington, Massachusetts 01803

Attention: Alan Fisher, Chairman

Dear Mr. Fisher:

We are pleased to submit this recalculated non-binding indication of interest related to the potential acquisition (the “Acquisition”) of Neuphoria Therapeutics Inc. (“you” or the “Company”) by one or more managed investment funds and vehicles affiliated with Lynx1 Capital Management LP (collectively, “Lynx1” or “we”).

As you are aware, on November 10, 2025, we submitted an initial non-binding indication of interest (the “Initial Offer”) related to the Acquisition. As you are also aware, on November 18, 2025, we withdrew our Initial Offer due to the Company's public disclosures on November 14, 2025, that (1) it had increased its outstanding share count by 128% over a four-week period, such that it had 5,377,329 outstanding shares of common stock as of November 13, 2025 (whereas our Initial Offer assumed 3,298,042 shares outstanding) and (2) it was further registering an additional $20 million of securities for offer and sale under its at-the-market offering program. This registration indicated to us that there would be even further dilution to the Company’s existing shareholders. As we have previously stated, we have continued to stand behind the economics of our Initial Offer, but the Company’s share issuances since our Initial Offer made it impossible for us to determine a specific offer price that would capture the economics of those issuances. We understand however from the Company’s recent public disclosures that it has now ceased issuing new shares, and so we are pleased to submit a recalculated non-binding indication of interest. It incorporates the Company’s recently disclosed share dilution as well as the net cash proceeds to the Company from that dilution (based on figures in the Company’s public disclosures), and it supersedes the Initial Offer in all respects.

As such, based on the information publicly available to us at this time, Lynx1 (through its affiliated investment funds and vehicles) proposes to acquire all of the outstanding shares of capital stock of the Company for a price of $4.75 per share in an all-cash transaction (the “Recalculated Initial Offer”). This Recalculated Initial Offer preserves the all-in economics of the Initial Offer, as adjusted for share issuances since October 27, 2025, the Company’s more recent cash balance figure (as projected by us, based on the Company’s public filings subsequent to the Initial Offer), and the Company’s continued spending in defense of its proxy contest with us. The Recalculated Initial Offer constitutes a price per share premium of 16% over the closing price of the Company’s common stock on Nasdaq on November 7, 2025, which was the last full trading day prior to the submission and public disclosure of the Initial Offer. This is lower (on a per share basis) than the 27% premium of the Initial Offer due (directly) to the Board’s actions since our Initial Offer.

The Recalculated Initial Offer is based on (among other things) the following assumptions:

•	The Company will not issue any additional shares of stock during the pendency of its strategic-review process, through the closing of the Acquisition. Specifically, the Company will have 5,377,329 shares outstanding at the closing of the Acquisition, all of which will be shares of common stock.

•	The Company will have unrestricted cash and cash equivalents at the closing of the Acquisition, net of our estimate of projected wind-down costs, of approximately $28 million.

•	There will be no participation in the Acquisition by holders of stock options, warrants or any other non-common-stock securities of the Company.

Because our proposal includes an assumption about the amount of the Company’s net unrestricted cash at the Acquisition closing, any delays to our consummating the Acquisition that result in a reduction in the actual amount of net unrestricted cash could in turn result in a reduction in our Acquisition price. Also, as with our Initial Offer, because we have sufficient capital available to us to fund the Acquisition, our ability to secure financing will not delay our process and will not be a condition for us to close the Acquisition.

As we stated in the Initial Offer, we are also willing to explore with you a transaction in which we acquire a select asset of the Company rather than the entire Company, if you believe that such a transaction is preferable to the Company’s stockholders. This would be subject to our due diligence into the agreement with the collaboration partner and licensee to ensure that the Company’s interest in the asset would not be terminated in connection with the transaction.

This letter and the proposal herein are not intended to constitute an offer capable of acceptance and do not create a binding obligation (to negotiate in good faith or otherwise) on Lynx1, the Company or any of their respective representatives. Those obligations would arise only upon our entering into a definitive purchase and related agreements relating to the Acquisition.

As with our Initial Offer, we believe that this proposal represents a highly beneficial outcome for the Company and its stockholders and are excited by the potential benefits that the Acquisition would yield for all stakeholders. We appreciate your consideration of this proposal and look forward to hearing from you as soon as possible, but no later than 12:00 p.m. (noon), New York time, on December 5, 2025.

Please do not hesitate to contact me with any questions or requests for additional information. We and our advisors remain ready to engage with you.

	Yours very truly,

	/s/ Weston Nichols
	Weston Nichols, Ph.D.
	Chief Investment Officer, Lynx1 Capital Management LP
	NEUP@lynx1bio.com

Neuphoria Therapeutics Inc. SCHEDULE 13D/A