What should be management best response to complainant (staff / community member) after a harassment / corruption complaint is proved to be false?
There are several possibilities for this:
1. The claim was provably false and filed with malice.
In this case the response is usually dismissal and criminal charges where applicable
2. The claim was correct but not found to be harassment.
There is usually no disciplinary action for this unless its repeated
3. The claim was not supported by enough evidence either way
Same as #2
Do keep in mind though that this varies greatly by local laws, labour laws and company.
It greatly depends on local laws, but in general this would mean dismissal in my books if it was a malicious complaint. If I couldn't do it straight away for some reason, it would happen as soon as I could manage it.
If it was a misunderstanding (which seems unlikely) I'd still get rid of them eventually, but I'd be nicer about it.
This sort of issue is bad for morale. The longer it's in peoples faces being talked about, the worse.