This question is not about Conversation View. I have had that on, and still do, since I started using Gmail over 15 years ago.
There is an old answer, from 2013, that says all you need to do is have the same Subject text on the messages, and you can do that by forwarding the "moving" message using the subject line of the "target" message. That may have worked in older versions of Gmail but it does not work now. In fact, that is documented on developers.google.com.
I attempted to use the "Subject Header" solution without success. I even copied the exact text of the target thread and used that to change the Subject line of the forwarded emails, and they ended up in separate messages, they weren't even combined themselves into as single thread.
So I went looking and sure enough, there are more requirements than just the Subject line.
https://developers.google.com/gmail/api/guides/threads, this is advice on using the Gmail API for people developing Gmail applications:
In order to be part of a thread, a message or draft must meet the following criteria:
- The requested threadId must be specified on the Message or Draft.Message you supply with your request.
- The References and In-Reply-To headers must be set in compliance with the RFC 2822 standard.
- The Subject headers must match.
So I guess what I need is a work flow in which I start with a message in the target thread and somehow attach the messages want to move. Or I need to find a manual way to edit the