Is it permissible for someone who holds money belonging to another person, whose whereabouts are unknown, to give it to a third person who deals with the owner of the money, especially if there is no certainty that this person will deliver it to its owner, and particularly if this person is in financial distress and requested to take the money to return it?

Whoever possesses money belonging to another must safeguard it until its owner is found, or until it can be delivered to someone trustworthy who can pass it on. It is not permissible to hand over the money to an untrustworthy person. If one does so and the money is lost or damaged, then they are liable for it, because they have caused the loss of another's property.