When digital content is purchased through iTunes or the Apple App Store, it is linked to the account holder rather than any specific devices or computers. By signing into that account on any computer or any iPhone, previously purchased content can be downloaded again free of charge. Apple allows up to five computers on an account at any one time, and an iPhone can be synchronized with as many of those computers as required.
Launch the "Settings" application on the iPhone and open the "Store" option.
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Open the "Store" menu at the top of the iTunes window, and select "Sign In." Enter the email username viewed on the iPhone, followed by the account password. Click the "Sign In" button, and the computer will be signed into the same iTunes account as the iPhone.
Click the "Store" menu again in iTunes, and then select "Authorize This Computer." Enter the account username and password, and the computer will be authorized to share the iTunes account fully.
Connect the iPhone to any of the authorized computers using its USB cable, and click the "Sync" button to backup and synchronize all iTunes content between the computer and the device.