Hello all, 
I imagine this has been asked before, so please forgive my repetitious posting.  I have just renewed my US passport at the  consulate in Bangkok, and they have assured me that the letter to take to immigration regarding transfer of stamps from one passport to another will be included. What other documentation, other than that letter, will be necessary to move my extension from  the old passport to the new one? 
Many thanks, Evan
TLDR : Answer Summary
To transfer your visa stamps from an old passport to a new one in Thailand, you will need the letter from the US consulate, a copy of the old passport data page, a copy of your last visa and entry stamp, and a copy of the new passport data page. It is also recommended to bring a photocopy of your TM6 form if applicable. While some offices may require forms to be filled out, typically there is no fee involved in the process, but it may vary by location.