It's probably best to notify the SSA of this.
Although not exactly the same situation as your son, the SSA web site states :
Moving in with a relative could change your benefit amount. You must report any change in living arrangement within 10 days after the month the change occurs. If you do not report the change, you may not receive all money you are due or you may receive an overpayment. If an overpayment occurs, you would be responsible for repaying the monthly. Failure to report a change also could result in a penalty.
Report all changes by mail or in person at your local Social Security office or call us toll-free, 1-800-772-1213 7 a.m. to 7 p.m., Monday through Friday.
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