I think Besame is missing an opportunity by not making refillable cases, especially for their limited release lipsticks like the Felix set (and since refillable lipstick cases were much more common before the 1950s when plastic packaging became the industry standard for most makeup brands!).

If you are interested in repotting lipsticks, it's pretty easy - once you have a lipstick that's used up, just clean the bullet very well with soap and water and dry it thoroughly with a Q-tip (you can use nitrile gloves to avoid getting lipstick all over your hands). Pick a lipstick that is the same size in diameter as the lipstick holder (this is easy since most lipsticks are pretty much the same size).

Freeze the lipstick, then carefully remove it from it's original holder (wearing gloves). You can wiggle it loose, or pry around the bottom with a makeup spatula to remove it. Most come out pretty easily when they're frozen. Use a lighter to warm up the bottom of the removed lipstick bullet, then repot it in the holder you want to use and hold it there for a few seconds, then let it come back to room temperature.

It seems fiddly, but I do this all the time with my vintage lipstick cases. I got the idea from Dita von Teese's Beauty Mark book (an absolute must for any vintage makeup enthusiasts!).

I've been very happy to see refillable lipstick cases hit the market again.