Praise be to Allah, and peace and blessings be upon the Messenger of Allah and his family.
Firstly:
If someone travels westwards, and reaches his destination at the time of Zuhr, but he had already prayed Zuhr en route, he does not have to repeat it, because a prayer cannot be offered twice, and it is known that as he heads westwards, the time for the prayer will become later.
The same applies if he had prayed ‘Asr; he does not have to repeat it, whether he reached his destination at the time of Zuhr or ‘Asr.
For more information, please see the answer to question no. 22387.
But if he is in the mosque, and the iqaamah for prayer is given, he may repeat the prayer with the congregation, and it will be naafil (supererogatory) in his case, because of the report narrated by at-Tirmidhi (219) and an-Nasaa’i (858) from Yazeed ibn al-Aswad, who said: I was present with the Prophet (blessings and peace of Allah be upon him) during his Hajj and I prayed Fajr with him in Masjid al-Khayf, then when he had finished his prayer, he turned and saw two men at the back of the congregation who had not prayed with him. He said: “Call them to me.” They were brought to him and they were trembling (out of awe). He said: “What prevented you from praying with us?” They said: O Messenger of Allah, we had already prayed in our camp. He said: “Do not do that; if you have prayed in your camp then you come to a mosque where there is a congregation, then pray with them, and it will be a naafil prayer for you.” Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
Secondly:
With regard to fasting, it is not permissible for him to break the fast until the sun sets in the place where he is at the time of sunset. So if he reaches his destination when the sun has not yet set, it is not permissible for him to break his fast until it sets, even if that takes a long time, because Allah, may He be exalted) says (interpretation of the meaning): “Then complete the fast until the sunset” [al-Baqarah 2:187]. And because the Prophet (blessings and peace of Allah be upon him) said: “When the night comes from here and the day departs from here, and the sun sets, then it is time for the fasting person to break his fast.” Narrated by al-Bukhaari (1954) and Muslim (1100).
Based on that, when this traveller reaches Korea, and he finds that it is still the time of Zuhr and he wants to complete his fast, he must wait until the sun sets, and it makes no difference that the sun has set in Nigeria.
If he wants to avail himself of the concession and break his fast because he is travelling, he may do that, especially since the day will become very long with this change in time zone, and it will be very difficult to complete his fast, waiting until night comes in the new place. Then he should make up that day on which he broke the fast, after Ramadan has ended.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: There is a student in a city in America who told us his story, that he had to travel from the city in which he was studying after he had started to fast at dawn, and he reached the city to which he was going after Maghrib according to local time, but he realized that he had already fasted for eighteen hours, and his fast had not yet ended, whereas on normal days he fasted for fourteen hours. Should he carry on fasting, despite the additional four hours, or should he break the fast according to the time in the city where he is a resident? And on the way back, the opposite happened, meaning the number of hours he fasted was reduced from 14 by three hours (i.e., 11 hours).
The Shaykh replied: He should carry on fasting until the sun sets, because the Messenger of Allah (blessings and peace of Allah be upon him) said: “When the night comes from here” – and he pointed to the east – “and the day departs from here” – and he pointed to the west – and the sun sets, then it is time for the fasting person to break his fast.
So he must continue to fast until the sun sets, even if that means four more hours.
A similar situation in the Kingdom of Saudi Arabia is if someone travels from the eastern region after sahoor to the western region. The hours of his fast will increase according to the difference in time.
End quote from Majmoo‘ Fataawa Ibn ‘Uthaymeen (19/322).
Dr. ‘Abdullah as-Sakaakir said in Nawaazil as-Siyaam, No. 2:
If the fasting person travels just before sunset from his city, heading west, then sunset will be delayed for him, such as if the sun sets at 6 PM in his city, and at ten to six he boards a plane travelling westwards; the further he travels westwards, the longer the day will be, because the sun does not set until 8 PM in the west. So for one or two hours longer, the sun will still be there. What should we say to him?
We say: He should not break his fast until the sun sets, even if it means that he will fast for two hours more, or four hours, or five or more. But he has the choice: either he may follow the ruling for the traveller, and avail himself of the concession allowing him to break the fast, or he can refrain from eating if he wants to complete his fast, because the Qur’an set a limit for the fast (interpretation of the meaning): “Then complete the fast until the sunset” [al-Baqarah 2:189]. And the Prophet (blessings and peace of Allah be upon him) said: “When the night comes from here, and the day departs from here, and the sun sets, then it is time for the fasting person to break his fast.”
So as long as the sun has not yet set, that day has not yet ended for this person. Therefore he must refrain from eating until the sun sets, or avail himself of the concession of travel, and break his fast and make up that day later on.
End quote from: https://bit.ly/2Zq4574
Conclusion:
1. If the time for prayer begins and someone prays, then he reaches his destination, whether the time for that prayer has begun there or not, he does not have to repeat the prayer that he already prayed, because a prayer cannot be offered twice on the same day. If the prayer has been done in a valid way, he does not have to repeat it.
2. The fasting person should not break his fast until the sun sets, no matter how late it sets, if he is travelling westwards. It does not matter what time the sun sets in the city that he has left, so long as he was not there at the time of sunset before he left.
And Allah knows best.