Why isn't iTunes auto backing up iPhone, previous backup exists

I have a family member's iPhone 6+ sitting next to me that took a trip out a car window when traveling down the interstate. On Dec. 31 2014 the new 6+ showed up and I did a backup of their old iPhone 5 to my computer. I used that backup to transfer all that data to their new 6+ immediately after. Now 3 months later they bring me a broken iPhone 6+ with no screen remaining and I was hoping that it would auto backup the data to iTunes like it does every time I plug in my iPhone 6 or my wife's iPhone 5. But no... iTunes instead detects the iPhone as XXXX's iPhone and says"Latest Backup: Your iPhone has never been backed up to this computer." So with the phone locked and the screen not existing it is not letting me create a backup without entering the passcode on the screen. And no, the fingerprint reader part of the screen is gone as well so that can not be used either.

How can I get iTunes to detect the backup and HOPEFULLY automatically backup the iPhone like it should?