Is it permissible for a supplies manager to contribute to (the cost of) a car operating in the factory he manages, given that he signs an approval guaranteeing it will not cease operation, and knowing that the higher manager is unaware of his contribution?

The employee is entrusted with his work, and it is not permissible for your husband to exploit his position for his personal interests and those of his partner. Therefore, he must inform the factory owner of the truth of the matter so that the latter may decide what is appropriate.

As for the money earned from the car's work, if the work is like any other without favoritism, then it is lawful. However, if favoritism occurred, such as the car working without the company's need, or not transporting what others transport, then there is a forbidden element proportionate to the favoritism, and it must be returned to the company along with repentance.