Transferring the crew is allowed, but all of the extra effects caused by it will cease as soon as the possessed crew is separated from the possession source. It will revert back to its original nationality, it will take up cargo space again, and its point cost will apply normally. (ADDED: It does not return to its original owner.)
The same happens if the Possession ability is cancelled, except in that case you may end up having to eject some crew.
For clarification, this applies to the ability of Wraith (SS) and Captain Davy Jones as well, and not just to the “possession” ability of Papa Doc?
For reference:
PD: If an enemy ship is within S of this ship, you can use this ship’s action for the turn to try to possess a target crew on that ship. Roll a d6; on a result of 6, the target is immediately assigned to this ship. Its nationality changes to match the nationality of this ship.
Wraith/CDJ: Whenever any crew is eliminated, roll a d6; on a result of 6, assign the crew to this ship. Its nationality changes to match the nationality of this ship and it becomes linked to this crew.