You Your son should be able to:
- Backup the device to the new installation
- Transfer purchases into an authorized library
- Recover any other media using third party tools as suggested in this post from forum regular Zevoneer
- Restore the device from the backup
This process should switch the association of the device to the new library, preserving the data and settings for the apps.
May also be prudent to attempt a backup to iCloud directly from the device before starting... Settings > iCloud > Storage & Backup > iCloud Backup > On. It won't save any media but it would preserve the general account settings and documents in case anything goes wrong while trying to extract other data.