Can't restore music to iPhone from iTunes I have a family member that did something a bit carelessly (but with good intentions) and I'm trying to help fix it.

They upgraded their iPhone 4 to iOS 5, but they did it from a different computer/iTunes than the one their iPhone was associated and synced with.  This wiped out everything on the iPhone, of course.

Now I'm trying to help them restore data, apps, music, etc.  There was a device backup in iTunes on the old laptop so I copied the contents of the MobileSync folder between the two systems.  On the new laptop, I restored from backup via iTunes.  Then, I proceeded to download all previous purchases in iTunes (apps, music), and then tried to sync:


First I synced apps only. No problemo.
Then I added music to the sync settings. Houston, we have a problem.


When I try to sync music it says that the iPhone is associated with another iTunes library and the phone will be erased.  Ugh.  If I only try to sync apps, there isn't an issue.  But of course, they want their music copied back to the iPhone. :)

In short, how do I accomplish all of the following:


Restore important data from the iTunes device backup copied from the old laptop
Ability to sync all purchased/future purchases of music
Ability to sync all purchased/future purchases of apps


Thanks in advance!
Note: This is all done on a Mac. Just look up the PC equivalent of the following steps if required.

How to recover past information:

Option 1 - Restore iPhone 4 directly from old computer:


Connect iPhone 4 to old computer, open iTunes, put the iPhone in DFU mode, (while holding alt/option key) select Restore after iTunes has detected the iPhone 4 in recovery mode, and select the most recent backup of that iPhone 4.


Option 2 - Copy iPhone 4 backup from old computer, and place on new computer to recover:


On the old computer, go to ~/Library/Application Support/MobileSync/Backup, and copy the most recent backup of the iPhone 4 and transfer it to the new computer.
Connect iPhone 4 to old computer, open iTunes, put the iPhone in DFU mode, (while holding alt/option key) select Restore after iTunes has detected the iPhone 4 in recovery mode, and select the most recent backup of that iPhone 4.


How to create the ability to sync all purchased/future purchases of music and apps:


Open iTunes.
Sign out any pre-existing AppleID/iTunes Account once iTunes loads.
Sign into desired account of individual (your relative's I'm assuming).
In iTunes, select Store -> Authorize This Computer...
Rejoice!
Have your relative use iCloud for backup to make life easier in the future.


Let me know if you have any more questions, or need any futher explanation. Enjoy!