Strangely, data portability is very low priority.
There really should be some server support for this – but OTOH it’s not paramount. Theoretically, anyone could write a client app that harvests all of a user’s posts and comments into a local DB, and then recreate threads (not comments) in a corresponding community. It would have to add some metadata about the date of the original post. Not great, but could be done.
I think I can force a new instance to cache a copy of an old post simply by searching for the old post using the URL as a query. That would get a verbatim copy of the post (perhaps along with the whole thread) on the new instance. But of course from there the problem is that the new cached version is still associated to the previous (foreign) community. Without knowing the code, I would speculate that it would just be a matter of changing the community it appears in to a local one in the DB (though it would of course have to be done server side).