If he travels during Ramadaan to another country that started the fast at a different time, how should he fast?
Question

                If a Muslim travels during Ramadaan to another country where they started the fast later or earlier than his country, and he stays in that country until Eid, with which of the two countries should he break his fast?.
Praise be to Allah.
    If a man travels from one country to another where the 
    moonsighting was different, the basic principle is that he should start and 
    end the fast according to the country he is in when it is established that 
    the month has ended. But if that means that he has fasted for less than 
    twenty-nine days, then he has to complete the number, because the lunar 
    month cannot be less than twenty-nine days. This principle is based on the 
    words of the Prophet  (peace and blessings of Allaah be upon him): “When 
    you see it (the new moon) then fast, and when you see it then break the 
    fast,” and “The month is twenty-nine days, so do not fast until you see it, 
    and do not stop fasting until you see it.” And in the hadeeth of Kurayb is 
    says that Umm al-Fadl sent him to Mu’aawiyah in Syria, and Kurayb told Ibn 
    ‘Abbaas (may Allaah be pleased with him) that the people had seen the new 
    moon of Ramadaan on Friday night in Syria. Ibn ‘Abbaas said: “But we saw it 
    on Saturday night, so we will carry on fasting until we complete thirty days 
    or until we see it.” Kurayb said: “Is not the sighting and fasting of 
    Mu’aawiyah sufficient for you?” He said: “No; this is what the Messenger of 
    Allaah  (peace and blessings of Allaah be upon him) enjoined upon us.” 

    There follow some examples which explain this principle: 

    1 – He moved from a land where the people started fasting on 
    Sunday to a land where the people started fasting on Saturday, and they 
    broke the fast on Sunday after twenty-nine days of fasting. He should break 
    the fast with them but he has to make up one day later on. 

    2 – He moved from a land where the people started fasting on 
    Sunday to a land where the people started fasting on Monday. They stopped 
    fasting on a Wednesday after thirty days of fasting. He should carry on 
    fasting with them even if that means he does more than thirty days, because 
    he is in a place where the new moon has not been sighted, so it is not 
    permissible for him to break the fast. This is similar to the situation if 
    he traveled whilst fasting from a place where the sun sets at 6 p.m. to a 
    land where the sun does not set until 7 p.m. – he should not break his fast 
    until the sun sets at 7 p.m., because Allaah says (interpretation of the 
    meaning): 

    “then complete your Sawm (fast) till the nightfall. And do 
    not have sexual relations with them (your wives) while you are in I‘tikaaf 
    (i.e. confining oneself in a mosque for prayers and invocations leaving the 
    worldly activities) in the mosques. These are the limits (set) by Allaah, so 
    approach them not. Thus does Allaah make clear His Ayaat (proofs, evidences, 
    lessons, signs, revelations, verses, laws, legal and illegal things, 
    Allaah’s set limits, orders, etc.) to mankind that they may become 
    Al-Muttaqoon (the pious)”

    [al-Baqarah 2:187]

    3 – He moved from a land where the people started fasting on 
    Sunday to a land where the people started fasting on Monday, and they 
    stopped fasting on Tuesday after twenty-nine days. He should break the fast 
    with them and their fasting will have been twenty-nine days while his 
    fasting will have been thirty days. 

    4 – He moved from a land where the people started fasting on 
    Sunday and stopped fasting on Tuesday after thirty days, to a land where the 
    people started fasting on Sunday and stopped fasting on Monday after 
    twenty-nine days. He should break the fast with them, and he does not have 
    to make up one day, because he has completed twenty-nine days. 

    The evidence that he has to break the fast in the first 
    example is that the new moon has been sighted, and the Prophet  (peace 
    and blessings of Allaah be upon him) said, “When you see it, stop fasting.” 
    The evidence that he has to make up one day is the words of the Prophet  
    (peace and blessings of Allaah be upon him): “The month is twenty-nine 
    days,” so it cannot be less than twenty-nine days. 

    The evidence that he may continue to fast for more than 
    thirty days in the second example is the words of the Prophet  (peace 
    and blessings of Allaah be upon him), “When you see it, then stop fasting.” 
    So ending the fast is connected to the sighting of the moon, and if it is 
    not sighted then that day is Ramadaan in that place, so it is not 
    permissible for him to break the fast. 

    The ruling in the third and fourth examples is obvious. 
This is what we think is 
    the ruling with regard to this issue, and it is based on the most correct 
    view, which is that the ruling varies according to the moonsighting. As for 
    the view that the ruling does not vary according to the moonsighting, and 
    that when the moon is sighted according to the shar’i conditions in one place, all the people must start or end the fast, this ruling depends on the evidence of the sighting of the moon, but he has to start fasting or stop fasting discreetly so that he does appear to be going against the community.  End quote.