The smooth mag housing is correct for a 1940 date MP.40. However, those pics show me that MP.40 is refinished. Some of the numbers don't look right for an fxo. If I had to bet money, and I'd bet a lot, it's at best refinished and reblued, and at worst it is cobbed together, "restored" with some renumbered parts, and refinished.
Matching MP.40s (original matching that is) with the original finish are tough to find. This piece is not one of them IMHO, and if it is as I set forth, the "winner" overpaid by more than double what it is worth, which is a pretty tough lick when we are talking about over $10k too much.