Making slight progress I guess. I learned that the 16-17 WRX/BRZ uses a different style connector for USB that plugs into the back of the OEM Starlink unit:
So, ideally I need a cable with that connector on the one side, going to a female OEM Toyota style usb connector on the other - seen here in the lower left hand corner:
Then I would be able to hook up the OEM male connector in the FR-S to it. (shown directly above this text)