The quote is confusing, because it's not always clear which Hall brother "Hall" refers to. Edward Hall, who developed the Minuteman missiles, was the brother of Theodore Hall, the spy. After reading the source article: <https://www.thenation.com/article/world/ted-hall-espionage-f...>, I can annotate the quote with first names:

"journalist Dave Lindorff, writing in The Nation on January 4, 2022, obtained through the Freedom of Information Act, Hall's FBI file in 2021. This 130-page file included communications between FBI Director J. Edgar Hoover to the head of the Air Force Office of Special Investigations, Gen. Joseph F. Carroll, showing that Carroll had effectively blocked Hoover's intended pursuit of [Theodore] Hall and Sax, probably fearing that [Theodore] Hall's arrest would have, in the political climate of the McCarthy Era, forced the Air Force to furlough and lose their top missile expert, Edward Hall. Carroll, a former top aide to Hoover before he became the first head of the USAF OSI, ultimately allowed Hoover's agents to question Ed Hall on June 12, 1951 (with an OSI officer monitoring the interview). Within several weeks of that session, the Air Force, which had conducted and completed its own investigation into Edward Hall's loyalty (having their own investigators question him four times), promoted him to Lt. Colonel, and later Colonel, and elevated him from assistant director to director of its missile development program. The promotions were a clear slap in the face to Hoover. Ed Hall went on to complete the development of the Minuteman missile program, and then retired."