Abstract: A firearm conversion system has a uniquely designed, unitary shoulder stock adapter. The adapter is configured to fixedly attach to a specially provided shoulder stock at one of its ends, and, at its other end, to fixedly attach to the trigger housing assembly and pistol grip of a Smith & Wesson, Model 76 sub-machine gun. When properly installed, the conversion components create a newly designed sub-machine gun having a fixed, comfortable shoulder stock with a longitudinal axis in fore and aft alignment with the longitudinal axis of the adapter and the trigger housing assembly.