You are driving a truck and trailer with a common compressed air-braking system. What is the function of the handbrake valve control setting here?

You answered correctly. When you use the handbrake valve in a vehicle combination with a common compressed air-braking system, the towing vehicle is braked using its spring-loaded (parking) brakes, and at the same time, the service brake of the trailer is released. This ensures the towing vehicle cannot roll and the trailer does not remain braked, preventing potential damage to the trailer brake system. Understanding this function is important for safely parking and securing such vehicle combinations.