The Hollow Earth theory is/was a pseudoscientific idea that our world is actually on the inside of a large sphere. The "sky" points inward towards the center, where the "Sun" (a light source) is, while the "ground" points outward.
Let's assume that we have a planet the size of Earth, except that it is a hollow Earth. In reality, it's simply an Earth-sized cavity inside a larger body, notably, some sort of artificial megastructure. I had assumed that said megastructure was spherical, but clearly I should have stated it explicitly, so I'll do so now. The structure will have spherical symmetry and be as uniform as possible.
Is it possible to put a moon inside the sphere - somewhere between the central light source and the "ground" - and have it move in an "orbit" around the center? Would the moon crash into the ground, or would it be stable?
I'm almost positive that the moon can't be as big as Earth's moon, but I don't know a reasonable size. I'm fine with anything bigger than, say, Janus or Epimetheus.
Bonus question (not necessary to answer): Is the setup possible if the hollow Earth is non-spherical, i.e. ellipsoidal?