That Thompson looks like it could be the m1921AC of 1926
You can see the Cutts compensator as well as foregrip, ribbed barrel, top-situated charging handle, dropped stock, drum magazine, and selector switch. [Edit: also original rear sight]
However, it could be the m1928 if it has a lowered rate of fire (owing to a heavier actuator and weakened springs) and a military blued finish.
The magazine is a 50-round "L" mag, but without visible markings I don't see it being possible to identify.
Also the front sight was canted to the left, on the left of p39.