Final answer:
The most appropriate action is to schedule the private inspection with coordination from the construction team, making sure the customer is informed of the timing and any other important details.
Step-by-step explanation:
If a customer notifies you that they have a private home inspector, the appropriate response is to schedule the private inspection in coordination with the construction team. This ensures that the inspection is integrated into the construction timeline and can be carried out effectively without delaying the project. Communication with the construction team is essential to arrange an appropriate time for the inspection, taking into account the stage of construction and any safety considerations. It is also important to maintain an open line of communication with the customer to ensure they are informed about when the inspection can take place and to address any concerns they may have.