Is the profit resulting from paying a sum of money to a friend to purchase a car through the state, which has not arrived after 7 years, permissible (halal)?

This transaction is invalid according to most scholars, as it is neither a valid agency for a fee due to the unknown fee, nor a valid jua'la (commission) for the same reason. Furthermore, it is not a valid Mudarabah (profit-sharing partnership) because it is restricted to a specific commodity, which invalidates Mudarabah according to the majority. If the agency and Mudarabah are invalid, then the Mudarib (agent/partner) is entitled to a fair wage (ujrat al-mithl), and this wage is estimated according to prevailing custom.