What are the rings called where the engagement ring and the band slide together to become one?

[diamondheart]

I was looking at a setting that my gf''s sister has. It kind of looks like a Vatche on the side of the basket but the prongs arent intertwined. It is a 4 prong setting and on one side of the two prongs one is longer that extends to right. Then she can slide her bakd between the ring and make it one ring. Just wondering what style this is?

 

[Modified Brilliant]

Insert? Wrap? Enhancer? Guessing that this is what you''re looking for.

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