Change of Address

My mother is 92 years old and has moved to a new address. I have tried to help her change her mailing address with Social Security, but we are unable to change it on-line or by phone. Even though the information is correct (SS#, date of birth, mother's maiden name, amount of last check, etc.). We get a message that the information does not match what is on file and we cannot continue. Can we mail a change of address in a letter with her signature? If so, what is the address? I only find address change ability on-line or by phone. Help!