72 340 4 spd question

Be careful, it could very likely be an overdrive 4 speed..... not that there is anything wrong with that. Is it an aluminum case? Do you have any pictures? Being long tailshaft and from a 360 is the tip off......

Yes, long tailshaft 4 speeds can be made to work in an a body, they are the same overall length as a 727 auto. You will have to fab a custom shifter mount, there are instructions floating around the net.