the purchased items are tagged to the console that it was first purchased for and the account that purchased it. So I assume the stuff was purchased under his gamertag on that console?
If you're using the new Xbox, there's nothing to do except download your account to the new Xbox.
If he's getting the new Xbox, he can redownload his content to the new Xbox and also download his gamertag. That'd probably be the most beneficial way anyway because it would let you use all the downloaded content (since it was first purchased and downloaded to the old Xbox) and let him use the content as well on the new Xbox since it's assigned to his gamertag anyway. However, that means for him to use the content on the new Xbox, that means he has to have a persistent connection to Xbox Live while he's gaming. if his Xbox is going to be offline, then you should do a license transfer and transfer the licenses from the old Xbox to the new Xbox.