What is going on?
Jaw quivering is a form of trembling. Usually it is harmless.
Jaw quivering is especially common in older dogs (and people). In these individuals it usually is progressive but it almost never compromises quality of life.
Four-month-old puppies generally do not suffer from progressive jaw trembling. The shaking is more likely a transient issue that occurs as the puppy’s nervous system matures.
Rarely, a quivering jaw may be a sign of poisoning or a serious neurological disorder. However, I’ll bet that your son’s puppy is simply going through a phase. I don’t think you should worry too much about this matter.