There's a couple of things you could do. You could set up a user account for your son on your Mac and then transfer his iTunes content from his computer to iTunes under his user account on your Mac. By doing so, you could sync and back up his iPhone on your Mac under his user login. Alternatively, you could just run a backup on your Mac but be careful here. You must open iTunes and go into preferences for devices and turn off auto sync when connected before connecting his iPhone. Otherwise when the sync starts it will erase the data on his phone and restore from your iTunes. iPhones sync to one computer, one iTunes library. When you connect his iPhone and it is recognized in iTunes, control click the iPhone icon and select backup. Or you could just back up his iPhone on iCloud and not use the computer at all.
