Create ticket via API combine with mailbox

Hello!
We use Youtrack as a help desk system (version 2023.2.21228).
There is a project (helpdesk type) to which we add tickets through the mailbox and through a form on the website via the API.

Tickets and subsequent comments to them are created through the mailbox as written in the Youtrack description, everything is fine. When created via the API, the following happens:
1. a ticket is created via the API;
2. a comment from the support service is left on it and it is sent by mail to the address specified in the form when creating a ticket;
3. the user who created the ticket receives it in the mail, but when responding via mail to the received message in the system, it is not added as a comment to the existing ticket, but a new ticket is created;

I think the reason is that there is no entry in Processed Emails with a Message ID after sending the first response to the ticket, The Message IDs of only emails that created tickets are registered.

It is necessary that the user's first response via email to the support service's response to a user's ticket left via the API should be added as a comment to the existing ticket, rather than a new ticket being created.
Is there a solution to this problem?