I liked the Puzzle Gift Box of Zachary Lance, but wanted a bit more fancy outer finish to hide the layer lines.
This derivative has a fuzzy skin on the outer box, but also on the end part of the inner puzzle body so the fuzzy look of both parts matches when it's closed. For the inner part I've used a print settings modifier to add the fuzzy skin only to the grip area and not to the puzzle structure itself.
The inner storage compartment has a diameter of 29,5mm and a height of about 106,8mm. There might be slight variations depending on your tolerances.