While the iPhone automatically backs up when connected to iTunes, you might experience an issue backing up the device when attempting to synchronize it with a different iTunes library if encryption is set for iPhone backups. According to Apple, the iPhone that is set for automatic synchronization must be connected to the primary computer used to transfer content in order to automatically create a backup of the iPhone's content. Backing up your iPhone on an alternate computer requires manually backing up while iTunes is open, which saves the iPhone's backup to your computer.
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Double-click the "iTunes" application icon on your PC desktop, or click the "iTunes" icon on the Macintosh's Dock to launch the application.
Connect the iPhone cable to your iPhone and your computer, and right-click the iPhone's icon in the side window of iTunes.
Click "Back Up" in the pop-up menu next to the mouse's cursor to begin backing up your iPhone to iTunes. Type the iPhone's backup password into the pop-up window, and press the "Enter" or "Return" key on your keyboard to save the password. The iPhone's backup status will appear in the status bar at the top of the iTunes window.
Click the "Controls" menu on the iTunes window and click "Eject" on the drop-down menu to unplug the iPhone from your computer.