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?
Bonus question (not necessary to answer): Is the setup possible if the hollow Earth is non-spherical, i.e. ellipsoidal?