Final answer:
The FAA Form 337 for the installation of extended range fuel tanks in a Cessna model 310 must be given to the aircraft owner and a copy sent to the FAA Aircraft Registration Branch within 48 hours of return to service.
Step-by-step explanation:
After the installation of extended range fuel tanks in the baggage compartment of a Cessna model 310, as the approving authorization inspector, you are responsible for ensuring that the FAA Form 337 is distributed properly. The original signed Form 337 must be given to the aircraft owner, and an additional copy must be forwarded to the FAA Aircraft Registration Branch within 48 hours of the aircraft's return to service. The entries must be detailed and precise, making note of the modification and affirming that the work was completed in accordance with the applicable Federal Aviation Regulations (FARs) and with reference to the approved technical data. The significance of proper documentation and distribution cannot be overstated as it ensures compliance with regulations and maintains the airworthiness of the aircraft.