The Falcon/Axe of the Minotaur is a weapon of the Minotaur, referred to in the Archive as the “H of the Minotaur.” It is probably an axe, given the context of medieval Templar weapons, and is assumed to be magical because it belonged to a demonic boss.
After the Day of the False Master it is mentioned as a possible trophy: “the H of the Minotaur is on the floor, yes.” It is not clear whether the group takes it or leaves it behind.
Spanish entry: Hacha del Minotauro