Place the puzzle on a table; the inner piece must be removed without moving the outer piece (can be touched, but not moved).

The inner cone piece is typically one piece solid or hollow. I modified it to be a container for small messages, thus becoming a puzzle box.

The cone piece must be lightweight for the puzzle to be easy to solve. I printed mine in PLA with 2 layers at top and bottom, 1 layer walls, and 10% gyroid infill. With those parameters the inner cone weight 7 grams, and is plenty strong for the expected use. The puzzle works fine even when a (small) paper message is contained inside.

Release files include a smooth surface (opening less obvious) and a easy to grip version of the cone (opening obvious).

Onshape model. Example wood version (video shows solution).

I could not find an "official" name for this puzzle.

It seems to be known as "Turbin puzzle" or "Newton’s Gravity Defying Puzzle".

If you know other names, please post in the comments (and indicate where you learned it).