Final answer:
The correct system used by the Department of Defense for personnel accountability after an official disaster declaration is the Armed Forces Personnel Accountability and Assessment System (AFPAAS).
Step-by-step explanation:
Once a disaster has been officially declared, all Department of Defense (DoD) components are required to report personnel accountability using the AFPAAS, which stands for Armed Forces Personnel Accountability and Assessment System. This tool is specifically designed to account for personnel and assist in managing the aftermath of a disaster. It ensures that military and civilian employees, contractors, and family members who are affected by a disaster are accounted for and can receive necessary assistance.