What is the ruling on buying a car for which the buyer paid the full price in cash, then it became clear to him that its ownership belonged to a girl who had purchased it from the bank through Islamic murabaha?

If you purchase the car in cash from the dealership, the fact that the car was registered in the name of a girl who bought it from the bank via murabaha and then sold it to the dealership does not affect the validity of the contract, and there is no sin in that. Transferring ownership is a legal procedure that entails nothing, and the murabaha transaction between the girl and the bank does not affect your transaction with the dealership, even if there were some doubt in it. The general principle is to consider the transactions of Muslims as valid, and there is no harm upon you in purchasing the car.