Ammonia to tri substituted nitrogen
Until there's water present (I'm assuming that it's not the solvent), the proton can't come from water. The proposed intramolecular proton transfer would go through a 5-membered transition state, which is reasonable. If you don't like that mechanism, then two of the intermediates could transfer protons to each other. Depending on the concentration, one or the other or both could be occuring.

The exact nature of these proton transfers are difficult to prove and typically inconsequential, so you will often see "shortcut" mechanisms drawn which imply intramolecular proton transfer even when it is more unlikely than the one you show here.