You can't transfer content between accounts. You need to do a licence transfer with the account you downloaded the content to the new console.
In order to then play that content on you new account the profile that purchased the content needs to be on your console aswell.
[/quote]If he's done the license transfer correctly the purchasing account does not need to remain on the console.
For example I often game at my friends houses and take my tag with me. The others in my house who use my console are still able to use my purchased DLC while I, and my tag, are not there.
To do a License Transfer simply sign-in with the tag on the new console, go to My Xbox and pick the Avatar square. Then go to the Account Management panel and pick the Manage Account option. Here all you'll need to do is pick License Transfer.
Then you may need to set the content to download again. If the content is already on your hard drive though, all that will be grabbed are the new licenses.