Does the State Department offer sponsorship of graduate study for foreign officers? If no, are FSOs allowed to take time off to complete graduate study and then return to their tracks without redoing the application process?
Every year on the lists of available onward assignments there are a handful of academic opportunities, such one year master's programs at a few universities or assignments to one of the Defense Department's war colleges. They are available to mid-level officers. Since the opportunities are so few you should not count on them as a way of getting a graduate degree. The Department of State also has a student loan repayment program, which varies from year to year depending on available funding and for which only FSOs at hardship posts are eligible.
Here are some possibilities:
The Department's University Economics Training Program (UET) is designed for highly motivated mid-career FS-03 and FS-02 Foreign Service economic-coned officers, who have both outstanding work records and strong undergraduate preparation in economics and quantitative methods
The National Defense Intelligence College (NDIC) Master of Science in Strategic Intelligence (MSSI) program.
The U.S. Army War College (AWC) in its Master of Strategic Studies Distance Education Program.
Princeton Master's In Public Policy (MPP) Fellowship Program
Organizational Management (OM) Fellows Program sponsored by the George Washington University (GWU) College of Arts and Sciences Department of Organizational Sciences (OS) Fellows. The Organizational Management Fellows Program is a one-year Master’s Degree program.
Various DOD institutions such as the Industrial College of the Armed Forces, Air War College, and National War College where participants can earn Master's degrees.
Also, once tenured, Foreign Service employees may apply for Leave Without Pay in order to pursue advanced studies. Each request is considered on an individual basis.