I read other topics on this subject but I'm still a little confused. Here's My question.

 

I just got a new US passport but on the first of next month I have to get an extension of stay for a Tourist Visa. So do I go to immigration apply for the extension and have them transfer stamps there or do I have to go to the border to do the transfer?

 

 

Apply for the extension at an Immigration office. They will transfer your entry stamp as part of the process. 

You can do it all at the Immigration Office at the same time

 

1900 Baht for extension, 1 photo, forms

 

Depending on which office you use they may charge you 500 Baht to transfer your stamps into the new PP,  this is not a official charge, it should be free