Hello and hope you are doing well.
Shuddering or restless in sleep could be due a sleep disorder. These disorders can be like obstructive sleep apnea, wherein during sleep there is an obstruction to air flow due to laxity of the throat muscles during sleep and this could cause restlessness. Hence for therapy CPAP (continuous positive airway pressure) is used to keep it patent. Another cause could be an entity called restless leg syndrome, where there is an odd sensation in the legs during sleep causing the individual to move, which relieves the sensation. These disorders can cause inadequate sleep leading to fatigue and daytime sleepiness. So, I would advise him to consult your primary care physician for further evaluation. He may then ask for a sleep study called polysomnography for further evaluation.
Hope this helped and do keep us posted.
This is a fairly common aspect of sleep. The mind is overactive whilst dreaming due to prior stimulation, its nothing to worry too much about. I had a similar thing but once removing simulants such as caffeine, tv, laptop for about an hour before bed, as well as using a memory foam mattress to support your boyfriend whilst he's sleeping, which can lead to a relaxed state prior to sleep, eliminating the shaking and overactivity of the mind