When you claim this expedition, deal 2 damage to the opposing mothership or destroy a base an opponent controls.
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Explained
When you claim this expedition, deal 2 damage to the opposing mothership or destroy a base an opponent controls.706.6, 301.7
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). Choose when it happens: your opponent's mothership, which takes the damage, or one of their bases on board, which is destroyed whatever its hull. With no base, the mothership takes it. A mothership left with no hull loses the game (705.7e).
Distance 2 · Spoils 1304, 706
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 2 progress claims it and gains 1 spoils.