Wrong 4-speed?

Is it possible to have a B/E-body 4 speed installed in an A-body? I've bought a 68' 383 4spd Dart years ago and pretty much parked it. The shifter was an aftermarket and installed wrong. Only 1st and 2nd worked, and that's how I limped it home using two gears. I finally decided to work on it and noticed the previous owner swiss cheesed the transmission mount and the trans is sitting cocked off to one side. I don't have any experience or knowledge on 4-speeds, any info. or solutions would be greatly appreciated. The trans. has 3 levers and no overdrive.