I'm not sure what actual letters like this are supposed to achieve (besides protecting his ass I mean). Are employees supposed to stand beside their fallen leader, are they supposed to go about their business differently? Anybody having affairs with subordinates can't be trusted to make good judgement calls with respect to internal leadership / delegation, at least it wouldn't seem so to me.
It sounds like your problem lies more in his mistake, not in coming clean about it. Him being the one to do that takes any influence the woman had over him away.