What is the Islamic ruling on the action of a person who earned money from someone else's trade without their knowledge, and is this money considered permissible (halal) or forbidden (haram), and is he obliged to compensate the injured party?

If your friend deceived you about the price and told you something contrary to the truth in order to take the price difference for himself, then this is not permissible for him. He must pay you the difference, due to the Prophet's (peace be upon him) saying: "Whoever deceives us is not of us," and his saying: "Deceit, treachery, and betrayal are in the Hellfire." He is your agent in the purchase and is not allowed to take any part of the price for himself. What he did is forbidden and is not approved by the Sharia, and you have the right to demand from him what he took unlawfully.