Use a threaded 1-1/8" headset, because that belongs to your frame and fork.
Slide the 1" shim / sleeve / piece of steerer tube into the 1-1/8" steerer tube and then the quill stem into the shim. Then tighten the stem.
Or, slide the shim over the stem, both into the steerer tube and then tighten the stem.
So, you just put the 1" stem into the 1-1/8" fork/steerer tube and use an additional 1" to 22.2mm shim.
Use a threaded 1-1/8" headset, because that belongs to your frame and fork.
Slide the 1" shim / sleeve / piece of steerer tube into the 1-1/8" steerer tube and then the quill stem into the shim. Then tighten the stem.
Or, slide the shim over the stem, both into the steerer tube and then tighten the stem.
So, you just put the 1" stem into the 1-1/8" fork/steerer tube and use an additional 1" to 22.2mm shim.
Good luck.