Praise be to Allah.
They should fast with the people and break their fast with the people, and they should offer the Eid prayer with the Muslims in their city because the Prophet (peace and blessings of Allaah be upon him) said: “Fast when you see it (the new moon) and break your fast when you see it, and if it is cloudy then complete the number (of days – i.e., assume the month is thirty days).” (Agreed upon). What is meant by this command to fast and to break the fast is if the sighting is proven by the naked eye or by means that help the eye to see, because the Prophet (peace and blessings of Allaah be upon him) said: “Fasting is the day when you (i.e., the Muslim community) fast, iftaar is the day when you (all) break your fast and adha is the day when you (all) offer your sacrifice.” Narrated by Abu Dawood, 2324; al-Tirmidhi, 697; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi, 561).
And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and upon his family and companions.