Is it permissible for a Muslim to fast Ramadan or break their fast with a country other than the one in which they reside?

A Muslim relies, for his fasting and breaking of the fast, on the sighting of the moon in his own country, provided that the reliance is on the Shariah (Islamic legal) sighting and not the astronomical one. This is based on the saying of the Prophet, peace and blessings be upon him: "The fast is the day you fast, the breaking of the fast is the day you break your fast, and Eid al-Adha is the day you offer your sacrifice." It is not permissible to rely on the sighting of the crescent moon outside of one's country if one's country relies on the Shariah sighting.