Final answer:
The primary communications net used by an observer to send FA calls for fire under decentralized observer control is the Fire Direction Net.
Step-by-step explanation:
Under decentralized observer control, the primary communications net used by an observer for sending Field Artillery (FA) calls for fire is the Fire Direction Net. This net is specifically designed for the purpose of transmitting fire commands fire control data and fire requests from observing posts to the fire direction center (FDC).
The swift and accurate communication via the Fire Direction Net is critical to the effectiveness of artillery support in a military operation.