New XBOX Live Membership link to offline gamertag

So I am new to all this and am utterly confused.  My son has been playing offline and has a Gamertag already set up.  Today as a surprise I went out and got him xbox live 3 month membership, came home, set him up an account, linked to my new parent account. Activated the membership to his account and set up the wireless on his xbox.  He came home longed on, and we found where to log in to the profile I created. But of course under the profile he had created are all his saved games and stuff.  So when he plays with it he is not on the membership I paid for. How can I get his gamertag moved over to the 3-month membership account I just created?