Battery on the 4s was the original from November 2011.
Very smoothly. Only a couple of snags.... I managed to be careful and still drop the ground contact piece on the carpet, but thankfully found it pretty easily. The other thing was that the battery cable has a fold in it that needs to be pushed down between the battery and the logic board so the connector is flush with the board and can be snapped on, but when I went to gently push that cable down with a spudger, I saw a tiny spark go from the cable (not the connector; the folded part of the cable that I was tucking down) over to the logic board. No ill effects noticed, but I was surprised that when I wasn't using a metal tool, the cable and the board exchanged electrons. Static? Be careful... maybe put something non-conductive along the logic board while tucking down that cable fold.
Just go slowly and carefully. I used a headband-style magnifier with a bright white LED light, and it makes things much, much easier with that magnification.