I recently wanted to be able to save a whole iMessage conversation thread. I have my iMessage on my iPhone and Mac, I did LOTS of googling and was only coming up with various software to download and then buy the full version to be able to get more than last 10 messages.
I then found the print option..
On the Mac you need to scroll to the top of where you want to save or print from.
Then go to Messages – File – Print…
The on the pop up, bottom left where it says PDF, select Save as PDF
Make changes to file name / location and then save.
You then have a PDF copy of your whole iMessage conversation.