Move? Not that I know of. Copy, yes, in principle. I wrote a backup routine that writes to a SQLite database. (Search this forum for SQLite.) It preserves row-ids.
When adding a row to a new table, of course, brand-new row-ids will be created, guaranteed to be different from the original. So, if there are any references to such a row, via row-id, you’d need to translate those references (row ids) from the old scheme to the new.
Of course, once it’s copied, you could delete the original data, so I suppose that would count as a “move”.