Save Your Personal Messages
One way would be as files of individual Web pages. I'd recommend saving as HTML only.
I just want to report that does work. Many times I've had the experience of "saving" a Web page only to find out it wasn't a static page in HTML, but just pointers via scripting to programs that would assemble the page freshly, so you actually need online access to the material to read it, and if that's gone you're out of luck. The personal messages pages here are in fact static pages laid out in HTML, so no such problem.