IOS – How to restore the iPhone as a new phone with the same OS version

you need to reset the phone to factory settings so that iTunes think's it's a new phone

it will then ask you if you want to restore from a previous backup and you can restore from any of them that are still on the system.

The official answer to this is no, you can not restore to a previous version of iOS other than the current one available from Apple. This is because iTunes is attempting to obtain tokens from the Apple signing servers to authorize the device when restoring.

The non official answer is yes, but requires some technical skills using iFaith. Post back if you require assistance down this path.