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If you start fasting in a country, then you travel to continue your fast the rest of the month of Ramadan in a different country, and the breaking of the fast [Eid day] comes later in the country to which you have traveled, then you should continue to fast with them until they break the fast, even if that is more than thirty days.
The evidence for that is because Abu Hurairah narrated that the Prophet (peace and blessings of Allah be upon him) said:
“The fast is the day the people fast, the breaking of the fast is the day the people break their fast, and the sacrifice is the day the people sacrifice.” Reference : Jami` at-Tirmidhi 697, which means that you always follow your locality when it comes to starting or ending the fast
However, when a person travels from a land where the onset of the month comes later to a land where the onset of the month comes earlier, then he should break the fast with them, and make up any remaining days he has missed in Ramadan later on.