My 91 year old mother received social security and Medicare part A. Who should report change of address?

Your Mom is in NH? Are they her payee for SS? If so, then Medicare and SS should know her changes. Is she on Medicaid? I assume she is since part B is usually needed. My husband's company pays for his insurance after retirement but he had to get part B with Medicare. If she is private pay and your are SS payee you need to contact SS about the change. They contact Medicare I think.