You cannot transfer to another person's AMEX accounts. However, most, if not all, AMEX partners allow transfer from anyone. Therefore, all you have to do is have your son link your respective account numbers and transfer directly into you and your wife's accounts.

Although, looking at the Delta promotion, it does require first time transfer and seems to be restricted to only one transfer. In that case, you may be out of luck as far as sharing points is concerned. You may want to try doing a point advance for 25K points instead.