Ramadan is the blessed month in which Allah orders Paradise to be well-prepared for righteous Muslims. The blessings of this month are abundant. One of the best things of the Islamic Sharia is that it does not call for rigidity. Therefore, if one performs fasting from one country and then travels to another, then he or she is to follow the fasting of the country to which he traveled. He is to follow the Muslim community in that country upon ending his fasting and celebrating the `Eid.
On this issue, Sheikh Ahmad Kutty said,
If you began fasting one day earlier in one country and ended up in another country for `Eid Al-Fitr, where they started a day or two late, then you do not fast, but simply observe `Eid with them. You are not allowed to eat and drink in public, however, in order to observe the sanctity of Ramadan.
Having said this, I must add, the above answer only applies if you have already completed 30 days of fasting. Otherwise, you should fast with them.