A long time ago, as a new Occupational Therapist at a major teaching hospital in Boston, I met a young patient who had a brachial plexus injury due to a bike accident. He had no use of the arm and eventually did choose amputation AND was committed to serious rehab inpatient, then ongoing outpatient, to learn one-handed techniques (self care, everyday living, and job skills) and be fitted for and learn to use a prosthetic device successfully.
I suggest making an appointment with a Physiatrist (a specialist in rehabilitation) and see how it goes. For best results, your son would need to be committed to doing the rehab and finding a way to go to a large well-recommended rehab facility, the large ones have lots of experience in amputation rehab.