Expanding on what lllaass said, an iTunes gift card is not "associated" with an iTunes Store account, per se. When you buy a gift card, it has a code on the back that is redeemed in a user's iTunes Store account. The value of the card is added to that user's iTunes Store account and the card is no longer worth anything and can be discarded. Therefore, as lllaass said, there is nothing on the card to "refill".
So if you want to add credit to your son's iTunes Store account, you need to purchase either a physical gift card or electronic gift certificate (the latter would be purchased through your own iTunes Store account and you could send the gift to your own email account) and then redeem the relevant code in your son's iTunes Store account.
You could also try a refillable "credit" card, setting that up in your son's iTunes Store account, but most such cards have no billing address associated with them and hence may not work in the iTunes Store.
Regards.