Is it obligatory to give money that was taken with the intention of delivering it to a specific person, but was spent on oneself, to the same person despite their need no longer existing, or is it permissible to give it to another needy person?

If the donor specified a particular person to whom the money should be given, you were obliged to give it to that person, and you erred by spending it on yourself. The action of an agent that contravenes the principal's instructions is considered suspended until the principal either approves or rejects it. You must inform the donor of what happened; if he forgives you, then all is well. However, if he demands the money back, you are obligated to return it to him, because you are responsible for the money due to your transgression. Do not spend the money on another needy person without the owner's permission, and promptly return the money to him or seek his forgiveness without delay.