Wouldn't it make sense to find a mortar at a temple?
Come to think of it, why are there rabbits on the Moon?
There actually is another story about that, but...
In that case...
To put it simply, a rabbit burnt itself as an offering to a certain old man...
and as a reward from Buddha, its soul was allowed to ascend to the Moon...
Such a sad story......
I see... So Buddha-sama called the rabbit to the Moon and gave it a mortar and mallet.