what sort of fence is he putting up then? Not a concrete and panel one obviously, if he is gonna damage your fence or compromise it's stability I would say no he can't, there was a comment made here the other day about a neighbour adding plantholders to his side of a shared fence but that wouldn't cause any real problem, but a fence is not necessarily a weight bearing structure, I think this is a difficult situation and you need to clarify a few points about the type of attachment and frequency along the run and who would sort out any damage or subsequent weakening of the existing fence.