Hmm. It seems like there should be more studs (on 16" centers) in that wall. Is there some sort of large beam at the top of the wall hidden from view?
At a minimum, you are going to want to frame in the window better than you currently have for the AC unit. And while you are at it you might as well make the window larger and at the right height too. By doing something like the examples below, you can use the window framing to support what looks like a nailing board to me (it is weird that they are horizontal instead of vertical). I would probably just cut out the rotted section and connect it to the side of the vertical window framing. You will need to do the same for the other horizontal boards too, though you may need to splice in an extension once all of the rot is gone.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.
