How to take a full length screenshot of the iPhone Messages app?

Stich It! is the App you're looking for I believe.

There is no other way without venturing into the adventures of jailbreaking your phone, and even in doing that I make no promises that something to save your conversation exists already. The ability to view the output of Messages.app is otherwise completely protected in a normal iPhone software setup, except to a full screen screenshot. You will have to take a series of screenshots, and stitch them together via photo editing software.

There may be stitching apps on the iPhone that can do the editing part appropriately (some kind of panorama software?), but you will still have to take screenfuls of screenshots manually.