The bottom line is that a 750 mile object of 4% the mass of the Moon, colliding at the far side of the Moon (as suggested in this article) would have had a very noticeable effect on the Moon's orbital trajectory around the Earth, providing an eccentric elliptical orbit, make it non-tidally locked, and most importantly would be sending the Moon on a spiral towards us, rather than away from us as we are currently seeing.
If the 750 mile object were in the same orbit as the moon, it would have the same orbital velocity as the moon. With a very small difference in velocity between it and the moon, it wouldn't change the moon's orbit much at all. Since the theory is that the smaller moon would have started in either the L4 or L5 Earth-Moon Legrange points, they would have had the same velocity.