Is the fast of one who broke his fast with another country after fasting the Day of Doubt on Saturday valid, even though his own country, Egypt, announced that Saturday was a mistake and that he must fast with it, or is he required to make up the day?

The Mufti's statement that sighting the crescent moon in other countries was an invalid error is refutable, because it was confirmed by the testimony of trustworthy individuals. The error lies in relying on astronomical calculations. Your fasting with another country and your reliance on the confirmation of the sighting there is correct, and you are not required to make up the day you broke your fast, especially if you adopt the view of the majority, which holds that fasting is obligatory for all people if the crescent is sighted in one country.