In this weekend's game, we faced a situation we couldn't quite agree upon.
Jim Culver had passed his individual Personal Story, so that "Sweet Harmony" was in play ("Each time an UNDEAD monster appears in Arkham, Jim instead immediately claims it as a monster trophy").
Then, in the Mythos phase, "Museum Haunted" was revealed: "Collect up to 2 Ghosts (...) Place them in the Miskatonic U. streets. Investigators who destroy one of these Ghosts before the end of next turn may draw one Exhibit Item.(...)."
Since Ghosts are Undead monsters, Jim Culver immediately claims them with his "Sweet Harmony" as soon as they appear on the board.
Our question was: Does he get the Exhibit Item by simply claiming them with his special ability, even without a fight, ie. without destroying them? Does his claiming count as "destroying" the monsters since they are removed from the board?
Thank you!

