What is the ruling for someone who began their fast in one country, then traveled to another or vice versa, and the country they moved to started fasting before their home country by one day or after it by one day?

Imam al-Nawawi has said as well as Sheikh al-Ramli in commenting on Imam al-Nawawi’s words in his famous juristic book Al Minhaj:

“ Whoever has traveled from a country in which the new crescent has not been sighted ‘to another country in which the moon was sighted, then he breaks his fast with the later. Whether the person has fasted twenty eight days meaning that Ramadan is missing a day and he has Eid on the twenty ninth day of his fast or he has fasted twenty nine days so Ramadan is complete, “he makes up a day” if he has fasted only twenty eight days since the lunar month can not be such, however if he fasted twenty nine days then there is no expiation needed since the lunar month could be such.

For this reason we see that it is best for the person traveling to follow the moon sighting of the country he is going to. If the amount of days he has fasted is less than twenty-nine days then he should fast an extra day after breaking his fast with the Eid celebration. If however, what he has fasted has reached thirty days, and the country he has gone to is still fasting, then he should withhold from eating, drinking and the like, but not with the intention of fasting as the lunar month never exceeds thirty days and is never less than twenty-nine days. However, he withholds from eating, drinking and the like so as not to harm or bother his fellow Muslims and to prevent social unrest among people who are ignorant of religious legal rulings.

God is most high all knowledgeable.