It says in Fataawa al-Lajnah al-Daa’imah, 10/9:
Zakaah should be given to those whom Allaah has said it is for, as He says (interpretation of the meaning):
“As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al-Masaakeen (the poor) and those employed to collect (the funds); and to attract the hearts of those who have been inclined (towards Islam); and to free the captives; and for those in debt; and for Allaah’s Cause (i.e. for Mujaahidoon — those fighting in a holy battle), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allaah. And Allaah is All-Knower, All-Wise”
It should only be given to those who are obviously Muslims, because the Prophet (peace and blessings of Allaah be upon him) said to Mu’aadh ibn Jabal when he sent him to Yemen: “Tell them that Allaah has enjoined upon them charity [i.e. zakaah], to be taken from their rich and given to their poor.” The more pious and righteous the poor and needy to whom it is given are, the more deserving they are than others.
The basic principle with regard to zakaah is that it should be given to the poor in the land where the wealth is, because of the hadeeth mentioned above. But if there is a need to transfer it elsewhere, such as the poor in the land to which it is transferred being in greater need, or because the giver has relatives who are poor, etc, then it is permissible to transfer it.
And Allaah knows best.