Praise be to Allah.
It is the same night, even thought it starts at different times in different countries. So in the Arab lands it begins when the sun sets in those countries, and in African countries it also begins when the sun sets there, and so on. Whenever the sun sets in a people’s land, it has begun for them, even if that process lasts more than twenty hours. So for one group of people their night is regarded as Laylat al-Qadr, then for the next group of people, their night is regarded as Laylat al-Qadr. And there is no reason the angels cannot descend to one group of people and also another.
And Allah knows best.