Lost Mole Recovery

It happens for the player who claims it, whoever launched it, and at once: claims happen in the battle step, after the crew destroyed there are gone (706.6). You see only the non-unique Moles in your hold, not its order. The one you take comes on board under your control, at no cost: it isn't deployed, so nothing that waits for a deployed crew happens, and it is new only if it comes in a watch. Then your hold is shuffled. You may take none, and then nothing is shuffled (801.10b).

In your own watch, while this card is in your scrapyard, you may pay the cost to put it on board. It isn't deployed: no one can react to it. It is launched again in the middle, with no progress.

Crew dispatched here on their own turn make progress, whoever launched it; on the opponent's turn they can only fight (706.3a). The first player to reach 3 progress claims it and gains 1 spoils.