Welcome!
I suggest you have your mother call the credit card issuer and first ask if they report AUs to the 3 credit bureaus. If they don't, it's a waste for you to be added. If they do, you will need to give your SSN so that the account appears on your credit report. Your mother will need to call them (some credit card issuers let account owners do this online) to give your info to get authorized user status; they're not going to just take your word that she has approved you!
Once you've been added, make sure she continues to have a good payment history by always paying on time.