Yes, your intentions are certainly laudable. I discovered, amongst my husband's belongings, after he passed away, an unconnected to the family, a Family Bible. After much searching, both here and elsewhere, I found the family it really belonged to. Once in contact, they kindly gave me their address, I, at my cost posted the heavy tome to the descendant. Sadly, there was not a thank you, or an offer to refund the cost.
I would be absolutely delighted to received a Family Bible belonging to my ancestors, however this is now very unlikely.