I've seen many posts about how you can't install a window AC unit through the wall. However, I have the opposite question. Can you install a through-the-wall AC unit in a window? It seems like someone would have created the hardware to do so, but I can't find it.
Specifically, window AC units have a bracket on them that secure them when the window closes on them. Essentially, I would be looking for a sleeve like you have in the wall, but with the appropriate hardware to mount in a window.
I know it's not as efficient as a window AC unit, but we moved into an apartment without a wall sleeve, so we would rather not buy another unit.