P.P.S. The fingerprint sensor flex cable connector probably could be manipulated into position with the tweezers from the tool kit and pressed down into place with the plastic screwdriver thingy, Just hover the back cover over it with your third hand (or a helper).
P.S. I got the battery and cover because the old cover was warped and separated, figured may as well replace the battery in a 2-year-old phone. Turns out, the battery was swollen and huge and it had pushed the back cover open. Not a good situation. So if your back cover is coming off, suspect that battery.
The flex cable for the fingerprint sensor is so short and delicate that it’s fiendishly difficult to locate and snap in. You only have a very narrow gap between the back cover and the phone, it wants to jump out of position if you misalign at all, and you can’t reach under there with normal size fingers. Not only that, it’s done with the rear cover adhesive in place so if that touches, it sticks.
I got it snapped on, and the flex cable broke at the same moment. So, no fingerprint sensor for me. Also, the new back cover arrived broken. If it was usable, the way to do it IMHO is to attach the flex cable first, then push the fingerprint sensor assembly on to the new back cover adhesive (it goes on from behind), then close the back cover.