OP's first sentence is only "borderline" acceptable - here's a chart showing that communicate to [someone] has largely fallen into disuse over the past couple of centuries.
If we accept that "semi-archaic" construction, note that it always requires a "secondary object" (some information conveyed - here, "the fact"). It's largely stylistic choice whether this is further qualified as being the information that was communicated, or which was communicated.
The second sentence represents the normal phrasing when there isn't a secondary object (i.e. - it's irrelevant that any communication occurred at all, and the specific information isn't mentioned). But in this case, it has to be the fact that [communication occurred]. You can't use which there.
Thus, given that which can only be used where the intended meaning is that some specific fact that was communicated is irrelevant, most native speakers will force that interpretation and overlook the "unusual" phrasing in the first sentence. Personally, I wouldn't - I'd say...
The [specific] fact[s] which I told Mona is/are irrelevant.
If you don't see a problem with to, consider "He communicated to me that I should leave". I think most people would agree this is stilted/formal/archaic.