What is the process for restoring iPhone from a backup that is NOT in iTunes?
Is the backup folder in the right location on the hard drive? iTunes only lists backups in the MobileSync/Backup folder. If you need to move the folder there, here's instructions for Mac and Windows for getting to that folder: https://deciphertools.com/blog/where-are-iphone-backups/

If it's in the right place, let's make sure it's not a version issue. iTunes won't show backups as a restore choice if they are incompatible with the version of iOS you're restoring to.


Open the iTunes Preferences (iTunes menu on Mac, and Edit menu on Windows)
Change to the "Devices" tab.


If you see the backup listed in Devices, iTunes recognizes the backup, and the issue is that the device you're restoring to is running a lower version of iOS than the device that made the backup.