The much larger smartphone battery is on the bottom left. Of course I re-assembled everything and the battery was then taped to the back of the whole thing. And even though that battery was on its last legs, this allowed me to charge once a week instead of once a day.

The trick is to preserve the tiny bit of electronics that is part of the original battery, and remove it from the new one, and solder 2 +/- wires from the old charging electronics directly onto the new battery. Of course it took ages to charge, but this way practically all 5V rechargeables are exchangeable.

This happened a couple years ago already, but I like this sort of community and just want to get the ball rolling.