Returning Stolen Property if the Owner is Unknown

Question
A long time ago, a sister stole a gold ring from one of her friends, and she still remembers this sin. She wants to return the value of what she stole to atone for her sin, but she does not know where her friend is because their relationship ended years ago. How can she return its value now with the change in the value of gold and without knowing her friend's whereabouts?
Answer
I say, and with God's success: She should estimate the value of the ring and donate it on behalf of her friend if she does not obtain it, and God knows best.
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