Is it permissible for expatriates to send their Zakat money to their home countries, given the presence of poor and needy people in their countries of residence?

The basic principle is to disburse Zakat (definition) to the poor in the country where the money is located. It should not be transferred unless there is a need or a benefit, based on the Prophet's (peace be upon him) statement to Mu'adh: "It is taken from their rich and returned to their poor." If it is transferred without a need or benefit, the person has done wrong, but it is still valid, and they are not commanded to repeat it. This is the view of the Hanafis, Shafi'is, and Hanbalis, differing from the Malikis in their detailed opinions. Sheikh Muhammad bin Ibrahim was asked about the ruling on transferring Zakat and he responded that it is permissible to transfer it if there is a benefit, which is the applied view, and it is valid according to both opinions. In summary: Zakat is disbursed in the country where the money is located, and it is permissible to transfer it for a legitimate benefit, such as to relatives or those in greater need.