Ticket response via API without creating duplicate ticket

I am trying to fix an issue where new tickets get created rather than a follow up to an existing ticket when using ticket API.
I have built an Azure Logic App that receives a new email and submits the HTML body to the "/api/v2/tickets.json" API endpoint in the comment: html_body attribute. The HTML contains the reference ID at the end which is also present in the "In-Reply-To" header. if I inspect the email directly. Unfortunately, I don't have access to that header field that I can work out, and even if I did, what attribute would I need to set with that value for it to add to the existing ticket rather than create a new one.
If I send an email with the HTML body, the reference is detected. The email doesn't contain the "In-Reply-To" header, so it must be finding the reference.