Differences in moon sighting between countries and its effect on those who travel from one to another
Question

Muslim brother observed fasting whole Ramdaan and attended Eid Al Fitr prayer too. Then he travelled towards east and reached his home country. The next day in his home country still the Ramdaan month is going on. Whether he has to observe fast again according to the home land or since he fast whole Ramdaan before his travel, no need to continue fast along with the local people of his home land.
Praise be to Allah.Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about a man who fasts twenty-nine days and attends Eid on the thirtieth day in the country where he was fasting, then on the morning of Eid he travels to another country when he is not fasting, but he finds the people there fasting. Should he fast or should he continue not fasting and regarding that day as Eid? 
He replied: You do not have to refrain from eating and drinking, because you broke your fast in a legitimate manner. So in your case it is a day when you are permitted to eat and drink, and you do not have to refrain from that. If you could not see the sun in one country then you traveled to another country where you could see the sun before it set, then you do not have to fast that day.  
And he was asked: if we start fasting in Saudi Arabia, then we travel to our homelands in eastern Asia during the month of Ramadaan where the hijri month comes a day later, should we fast thirty-one days, and if they fast twenty-nine days should we break our fast or not? 
He replied: If a person travels from a country where he fasted at the beginning of the month to a country where Eid al-Fitr comes later, he should continue his fast and not break his fast until they do. This is like the case where a person travels from his city to a place where sunset comes later; he should continue his fast until the sun sets even if that takes twenty hours, unless he breaks his fast because of traveling, as he is entitled to do. The opposite also applies, such as if he were to travel to a place where they have stopped fasting before he has completed thirty days – he should break the fast with them, and if the month was thirty days he should make up a day, and if it was twenty-nine days he does not have to do anything. He should make it up if he did less than a month, and if he did more than a month then he did more. And Allah knows best.
Majmoo’ al-Fatawa, 19.