I think an "invention" usually is done by one person or a small group that searches for a solution for a certain problem. But language was not created this way. It just appears and it also changes without anyone doing this intentionally.

I think the same goes with money. There was nobody who just said "these sea shells will now be used to trade everything against it". It's more like a habit that developed between more and more people until it was accepted by a whole society.

You could say metal coins and paper money where invented. But not money itself.