When the sun has set, it becomes permissible for the fasting person to break the fast, whether the muadhdhin has given the adhan or not. What counts is the setting of the sun.

If a person starts fasting in one country and travels to another where Ramadan began later, they must continue fasting until the local community observes `Eid. This may result in fasting 31 days. However, if they move to a country where Ramadan ends earlier, they should break the fast with the locals and make up missed days later.