Right now, there are several elements:

• Users — Mastodon deals with it by introducing a "Move" action that makes any followers switch from following the old user URL to a new user URL. A server export and import would be required for the user's subscribed communities, config, and profile data.
• Comments — This is where things get somewhat hairy, but possible; the new home server (instance) would need to re-publish the user's content as coming from the new user URL. Ideally there could be a similar "Move" or "Takeover" activity that an instance could broadcast for each content item, so they would get reattached to the new user URL.
• Interactions — Other user's responses, boosts, faves, etc. reference old content URLs, so instances should follow the "Move" and "Takeover" events and fix those accordingly.
• Lemmy Communities/Posts — This one's actually the easiest: communities are just a special user that boosts any message sent to the community. You can clone a community right now by simply creating a "community user" and having it boost the same messages as the "source" community. Then you can delete the original, or have it de-boost stuff, or keep both boosts, or whatever.

Extras:

• Cross-posting — A "community user" boosts a post from another (it's a pity we don't have this yet).
• Splitting a Post — Have the second community user boost a post with just some of the comment threads, while the original de-boosts them. Now there are two posts with maybe comments that maybe follow different instance rules, or fit better with different instance profiles.
• Post linking to a toot or comment — This would need some format change, but wouldn't be too difficult.
• Upgrading a comment to a post — This would require several of the previous features, but would allow moving off-topic conversations to their right place.