Yes, both are significantly restricted the moment someone goes into the SHU, and the limitations are more severe than most families expect going in.
Phone access drops to one 15-minute call per week. That is it. Whatever frequency of calls you were used to before the hole is gone, replaced by a single weekly window that has to count for everything. Make sure your number is active and you are available when that call comes because there is no rescheduling it if you miss it.
Messaging through JPay is not available in the hole at all. The tablet or kiosk access that makes JPay work in general population does not extend to segregation. That channel goes dark for the duration of the SHU stay.
What does still work is mail. Physical mail continues to move in and out of the SHU, which is why this is exactly the situation where postcards and letters become the most important form of communication you have. A letter takes a few days to arrive, but it gets there, and for someone sitting in a cell with almost nothing to do and very little contact with the outside world, a piece of mail is genuinely significant. Do not underestimate how much it matters.
If you want to make sure something is arriving for him consistently while he is in the hole, InmateAid can help you keep letters and postcards going out on a regular basis without the hassle of printing and mailing yourself. Staying visible through mail during a SHU stretch is one of the most concrete things you can do from the outside.