This is how I would do it

by Pepe7 - 4/9/12 8:10 AM

In Reply to: iPad backup and sync in a different computer? by prettypinksundress

First choice for me would be to turn on iCloud if you haven't already, and backup what you can using this method. Depending on how much content you need to back up, you might have to purchase additional iCloud capacity. YMMV. Look under Settings > General > About to see how much space is being used up currently on your iPad.

Second choice (or even something in addition to using the iCloud method) would be to use a third party software that lets you freely copy content from your iPad back to your son's iMac. Simply connecting and re-authorizing to the new PC/Mac will most likely trash your content you want to retain. There are a whole slew of choices for accomplishing this. Sites like iLounge.com give some decent reviews of the various software for this purpose.

I believe methods like the following are in practice more complicated IME. Others here will likely chime in on what their experiences are. See the following as one example:
http://www.howtogeek.com/104298/sync-your-ios-device-with-a-new-computer-without-losing-data/