Final answer:
The proper checklist action when an amber APU SOV message appears after the APU is shut down due to fire is to activate the fire suppression system, following the specific aircraft's emergency procedures. Restating the APU or ignoring the message is not appropriate.
Step-by-step explanation:
The subject of this question pertains to aircraft systems, specifically focusing on the Auxiliary Power Unit (APU) and emergency procedures. When an amber APU SOV message appears after the APU has been shut down due to fire, and the engine is supplying bleed air for air conditioning, the proper checklist action would not be to restart the APU or ignore the message. Given that the checklist would vary based on aircraft manufacturer and model, a standard practice in response to potential APU fire indications would typically include activating the correct fire suppression protocol which may involve shutting down the APU, if not already accomplished, and confirming that the fire suppression system has been activated or found in the automatic state. In this scenario, the most appropriate checklist action among the provided options is likely to activate the fire suppression system, assuming this has not happened automatically or was not performed during the initial shutdown of the APU due to fire. The response to the fire warning must be carried out in accordance with the specific airline's Standard Operating Procedures (SOPs) and emergency checklist for the type of aircraft in question. It is always essential to follow the aircraft's emergency procedures and guidelines as closely as possible during such events. Options such as ignoring the message or shutting down the engine providing bleed air are less appropriate until the fire indication has been properly addressed.