Can you install a shorter A body 833 into a 71-74 B-Body?

I'd agree with Rainy it's possible but you going to have a shifter location and driveshaft length issue.
With so many b-body unit out there I would think a trade be available.

An adapter for b-body trans into an A-body can give an idea for the other way I suppose.
http://www.bigblockdart.com/techpages/abconv.shtml