Can you identify this faucet reseating tool?

Could anyone please help me identify this fitting/coupling and it's use? Any help would be greatly appreciated.

It is the "guide" for a faucet reseating tool. It is tapered on both ends so it will "catch" and center itself on a variety of faucet openings. A picture of mine would have the reseating tool through it because I keep them together.

SO, it's not really a fitting, it is a tool guide.

I don't think so, if it were just the top part I could see it. If you turn the top part over, it will thread into the bottom part. The bottom piece actually swivels.

The picture that was added to my previouse posting is a "simple minded" version. The one you have is from a "Sexauer" faucet rebuilding kit. It is a more "precise" version and adapts to more valves. With the entire kit, you can do a better job of actually reseating valves rather than just make "flat" surface. Mine is from the 70s but I imagine it is still made.