You must act according to the horizon of the place where you are currently in. Hence, the Night of Qadr and also Eidul Fitr are determined on the same place.
Some grand religious authorities’ answers to this question are as under:[1]
Grand Ayatollah Khamenei (may Allah grant him long life):
You must act according to the horizon of the place where you are currently in.
Grand Ayatollah Makarem Shirazi (may Allah grant him long life):
Wherever you are, you should act according to the horizon of the same place. You must note that ‘night’ means that the shadow of part of the earth falls on the other part. Therefore, if the Night of Qadr starts in Mecca, the Night of Qadr continues until the shadow takes over all parts of planet earth. In fact, the Night of Qadr lasts for 24 hours. There is no more than one night throughout the planet.   
Grand Ayatollah Saafi Gulpaigani (may Allah grant him long life):
The Night of Qadr (Laylatul Qadr) is determined depending on when and which day you ascertained the beginning of the month of Ramadhan. The day of Eidul Fitr would then be determined. If the crescent is sighted on the night preceding the 30^th day of the month, the following day would be the Eid day; otherwise Eid would be upon completion of 30 days.

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