There cannot be significant amount of water on the moon, because Moon was once a ball of molten lava covered with thin surface. As impact basins were formed after collisions with fluid lava, we can make a safe argument that water was not able to stay with the moon even if it was once plentiful.

Which is asking where all these water of the Earth came from? Was Earth also ball of molten lava but somehow water stayed with the early Earth as atmospheric steam?