I found it much easier to reassemble if I put the battery assembly into the cover & insert the whole thing into the body. Otherwise, as noted, you have to pry the sides apart to fit the cover in place.
I replaced the stock battery with a 1000nAH battery. I believe the stock batteries were 600mAH. It runs fine, but when charging it continuously blinks. It never proceeds to a solid light & then off. I have not yet run it down completely, so I don’t know it it is charging completely.