No, the ring is not the same as the one in the other case you mention. How do you find this part? Patience and searching...it will likely take you more than the 1/2 or or so you've spent looking so far.
Alternately, the part is available from Omega, but you would have to find a watchmaker with an Omega parts account to purchase it from Omega, and they will likely want to fit it, and may require a full service.
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