So quick question Should you accept a ring from someone who cheated on you ... even when they said sorry (asking for a friend lol)

Depends on how you feel in your heart.

Explanation:

If they cheated, they've obviously done you wrong.

But! Taking into fact they apologized, and now are offering what appears to be a peace offering, I'd accept if you feel you truly know that person is attempting to heal the relationship.

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