Is one who takes a sum of money found by another person sinful, even though it is not his lost money, but the person who found it wanted to give it to him as compensation for what he lost?

Since the money taken is not the one you lost, it is not permissible for you to take it, nor is it permissible for the finder to give it to you, knowing that you are not its owner. The finder must announce it for a year. If its owner comes, he should hand it over to him; otherwise, it would be a betrayal of trust, and he would be responsible for the money.