Assuming that the elevator is a closed car (like inside most buildings) there would be little effect on the fly due to the movement of the elevator. With the doors closed the elevator, the air, and the fly are all one system together. The air moves up with the elevator as well as the fly. There is some force toward the floor due to the rise of the elevator which would affect the air and the fly (and the people in the elevator) but that would not significantly alter the Flys path.
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