Is it obligatory for someone who left Egypt on Ramadan 1st — which coincided with Sha'ban 30th in Egypt — to fast or to break their fast, taking into consideration that their fasting in Egypt would be considered a day of doubt, and their breaking the fast in Kuwait would mean an incomplete Ramadan fast? And does the same ruling apply to someone who travels on the day of Eid?

Your friend is not required to fast on the aforementioned Saturday due to Ramadan not being established for the people of Egypt. It is recommended for him to abstain from eating and drinking if he arrives in Kuwait and finds its people fasting. He must complete his fast if he arrives while already fasting. This is based on the opinion that different moon sightings (matali') have an effect, which is the preponderant view. However, according to the opinion that they do not have an effect, he must fast in Egypt with those for whom the month has been established. If the people of Kuwait break their fast after 28 days, he must break his fast with them and make up one day after Eid. If he travels to Egypt and they fast for 30 or 31 days, he must fast with them. The criterion for fasting and breaking the fast is the country where the person is located, based on the Prophet's (peace be upon him) saying: "The fast is the day you fast, and the breaking of the fast is the day you break your fast, and the sacrifice is the day you sacrifice." Scholars have differed concerning the "Day of Doubt" (Yawm al-Shakk). The Shafi'is specified it as the night of Sha'ban 30 when people speak of Ramadan but it is not known who sighted the crescent or if the person who sighted it is someone whose testimony is not accepted. The Hanbalis specified it as when the sky is clear and the crescent is not seen. The Malikis, conversely, considered it to be when the sky is cloudy. The Hanafis held that it is the 30th of Sha'ban if the crescent is obscured, or if one person sees it, or if two fasiq (sinful) individuals see it and their testimony is rejected.