Moving an existing account
Accounts can move to your PDS from another one, including from Bluesky's own servers, and keep their identity and followers.
Tell the person you invited to use a migration tool such as PDS MOOver, and to choose your PDS as the destination. You'll have to give them an invite code too, don't forget that part!
Handles
The moving account picks a new handle on your PDS during the move: under your PDS's domain, one of your extra handle domains, or their own domain (could also be their existing handle).
Large Accounts
If an account has a lot of media (we're talking multiple gigabytes of blobs), the import process may take a while to complete; you will also need to ensure you have enough blob storage quota on your PDS to house this new bounty of media brought by a migrating user. If you don't, the media import will stop. However, PDS MOOver supports resuming the media import, so you can add quota, and then tell the account owner to try resuming or choosing the "import missing blobs" option on PDS MOOver.