The "General" is appended to the typename (Surgeon General/Attorney General), as a modifier to the position granting it the "rank" of senior /advisory position. Therefore, you would just build the sentence as you would without "General" then add it in?
So "The surgeons' cups of tea" becomes "The Surgeons' General cups of tea"
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So "The surgeons' cups of tea" becomes "The Surgeons' General cups of tea"