Must someone who fasted in Jordan one day before the sighting of the crescent moon in Kuwait complete thirty days of fasting with the people of Kuwait, or should he break his fast on the day he completes thirty days, if that day is Eid in Jordan but not Eid in Kuwait?

Your ruling is the ruling of the country you will travel to. If they fast thirty days, then fast with them, and if they break their fast, then break your fast with them. Imam Al-Nawawi mentioned that if someone fasts in one country and then travels to another country where the crescent moon has not been sighted, and it completes thirty days, then it is obligatory for him to fast with them because he has become one of them.