Earth in the far past seems to have got it`s water from in comming asteroids in the very young solar system,so the moon could have got some too. That is after it was formed out of the planet earth after it was smashed into by a large rocky asteroid.Or so the scientists speculate. Other rocky planets,Mars for instance, has water albeit under the surface.And it seems that Mars had running water just a few million years or so ago,which is not so long in the age of the solar system.
historian