Final answer:
The Air Force Personnel Center (AFPC) is responsible for AEF sourcing of individual augmentees, Joint Manning Document authorizations, and managing replacements for long-term requirements.
Step-by-step explanation:
The organization responsible for Air and Space Expeditionary Force (AEF) sourcing of individual augmentees, Joint Manning Document authorizations, and managing replacements for 365-day or greater requirements is the Air Force Personnel Center (AFPC). The AFPC oversees the personnel aspects of the United States Air Force, handling the tasks related to the deployment and management of individual augmentees, who are members of the force reassigned from their normal duties to support operations as needed. It also manages documents and authorizations necessary for personnel operations, such as the Joint Manning Document, making it integral to the effective functioning of Air Force expeditionary operations.