Which service manages military post offices, mail terminals, and official mail centers?

The Military Postal Service is the correct choice because it is specifically organized to oversee and manage the handling of all mail for military personnel and their families. This service is responsible for ensuring the efficient operation of military post offices, mail terminals, and official mail centers. By maintaining these facilities, the Military Postal Service ensures that mail is processed, delivered, and managed according to military regulations and standards, allowing for reliable communication for service members, whether they are stationed domestically or overseas.

In contrast, the other options serve different purposes within the military's logistical and communication frameworks. Aerial Mail Terminals focus on the transport of mail via air, primarily facilitating expedited delivery rather than the overall management of postal services. Mail Control Activity typically refers to specific units that deal with tracking and managing the flow of mail within military installations. Activity Distribution Offices, meanwhile, are more involved with the distribution of supplies and articles rather than mail services. This distinction underscores the unique role of the Military Postal Service in managing all facets of military mail operations.