You can't have a second copy on board. Once you have claimed one, you can't launch another, make progress at your opponent's copy or claim it: it is scored only once.
Your Gliders have +1 firepower.301.3a, 304.5a
While this card is on board, every Glider you control has 1 more firepower, in your berth or dispatched, including Gliders that come on board later. Your opponent's Gliders don't get it. Once the expedition is claimed, it works from the logbook for the rest of the game, for the player who claimed it, whoever launched it: "you" is then the claimer (304.5a).
Distance 8 · Spoils 2304, 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 8 progress claims it and gains 2 spoils.