On which of the following occasions may an FCC-licensed amateur station exchange messages with a U.S. military station?

The correct scenario in which an FCC-licensed amateur station may exchange messages with a U.S. military station is during an Armed Forces Day Communications Test. This annual event is specifically designed to promote goodwill and showcase the capabilities of amateur radio operators. During this event, amateur stations are authorized to communicate with military stations and share messages, which helps facilitate the demonstration of amateur radio's value in emergency communication and public service.

Other occasions, such as Memorial Day or Independence Day celebrations, do not have specific provisions or structured events that allow for the exchange of messages with military stations. Although amateur radio can be part of local events and activities on these holidays, they are not recognized as formal occasions for communication with military stations. Propagation tests, while important for understanding radio wave behaviors, do not involve direct exchange of messages with military stations and are generally focused on evaluating signal transmission characteristics.