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Typical threadless adapter. It just happens to be that the headset is 1 1/8" threaded, not 1" like most frames.
The adapter can be used a quill to threadless adapter as well as a threadless extender according to the website:
https://bbbcycling.com/en/bike-parts/headset-parts/BHP-21
The design is pretty much the same as the other quill to threadless adapters I've used in the past.
You can see the wedge in this photo, like a normal quill stem.
Are you just planning to use it as a typical threadless adapter, above the threaded lock nut? That particular item is designed for extending threadless steerers, but I guess it'll work