Q: The Western Allies hoped that the Tunisian campaign and invasion of Sicily would weaken and topple Mussolini. After the July 1943 invasion of Sicily, the strategy paid off big when Mussolini was arrested at a meeting of the Fascist Council on July 25. Senior fascists, generals and the King grabbed control and yet the event seemed to have taken the Allies unprepared to instantly exploit the event. An Armisitice was signed September 3 and made public September 8 – 45 days(!) after the arrest. Why did the Allies not instantly send representatives to Italy to promise the new leaders ANYTHING they wanted to coax Italy to immediately switch sides (even if Roosevelt and Churchill might renege promises later). Also, the delay seems only to benefited Germany by giving it more time to react.
(in contrast: invasion of France to Armistice = 43 days)