What is the ruling on the ring that my mother found in her youth, and my grandmother did not return it to its owner? And how can my mother absolve herself and her deceased mother's conscience? And how is the value of the ring to be estimated?

The grandmother of the questioner is responsible for the ring because her daughter was most likely not an adult when she was given the ring to deliver it to its owner, but she did not do so. Thus, she is sinful and liable for the ring, as the Prophet, peace and blessings be upon him, said: "The hand is responsible for what it takes until it returns it."

Therefore, it is obligatory to pay the value of the ring to its owner, or to her heirs if possible. Otherwise, its value should be given as charity on behalf of its owner. The value to be considered is its worth on the day it was wrongfully taken into possession.