Hi Anneb
It is all about the timing, is your son able to wait for a transitional letter from DWP before moving? If he can then he would get transitional protection, if not he would loose out on the disability benefits.
The answer is yes, he has a sick/fit note, as he is in the support group, as long as his ESA claim does not stop, not even for one day, then he should be placed in the LCWRA group.
I would contact your local Welfare Rights Organisation;
advicelocal.uk , they will be able to take all his circumstances into consideration.
Gary