Hopefully Thai immigration is up to speed on this.
AU, USA, UK have stopped providing letter to request transfer of stamps. Perhaps there are others.
Think USA is supplying a statement that they do not provide any.
In any event should not be an issue.
There is a form available.
If you paste this into Google it will provide form.
1486548719379.doc Request to transfer the stamp to a new passport
https://aseannow.com/topic/1247977-transfer-visa-stamps-from-old-passport-to-new-passport-process/