The basic rule is that zakat collected in a region should be distributed among the needy of the same region. Ibn Abbas (one of the companions of Prophet Muhammad(ﷺ)) narrated:
The Prophet Muhammad (ﷺ) sent Mu’adh to Yemen and said, “Invite the people to testify that none has the right to be worshipped but Allah and I am Allah’s Messenger (ﷺ), and if they obey you to do so, then teach them that Allah has enjoined on them five prayers in every day and night (in twenty-four hours), and if they obey you to do so, then teach them that Allah has made it obligatory for them to pay the zakat from their property and it is to be taken from the wealthy among them and given to the poor.” [Refer Sahih al-Bukhari, hadith no. 1395]
Ibrahim ibn Ata, the client of Imran ibn Husayn, reported on the authority of his father:
Ziyad, or some other governor, sent Imran ibn Husayn to collect sadaqah (i.e. zakat). When he returned, he asked Imran: ‘Where is the property?’ He replied: ‘Did you send me to bring the property? We collected it from where we used to collect in the lifetime of the Messenger of Allah (ﷺ), and we distributed it where we used to distribute during the time of the Messenger of Allah (ﷺ).’ [Sahih Al-Albani, Refer Sunan Abi Dawud, hadith no. 1625]
According to Shaikh Mohammad bin Salih Al-‘Uthaimeen in Fatawa Arkanul Islam; it is permissible for a person to transfer his zakat from his country to another country if it is needed more in that country. If a person has relatives who have the right to receive zakat but live in another country, and he sends it to them, there is no objection to do so. Similarly, if the standard of living in the country is high and a person sends it to the country of his family which is poorer, there is no objection to that either.
But, if there is no benefit in transferring his zakat from one country to another, then it should not be transferred.
Allah’s Messenger (ﷺ) appointed Mu’adh to a position in Janad, where he remained until the death of the Prophet (ﷺ). When this occurred, he came to Khalifah Umar who reappointed him. He sent Umar one-third of the zakat collected from the local people, but Umar refused it and said:
“I did not appoint you to go there as a tax collector or as attribute (jizyah) collector. I appointed you to collect zakat from the rich and then give it to their poor.”
Mu’adh replied: “I would not have sent you anything (from the collection) if I had found someone deserving (over here).”
In the second year, he sent him half of the collected zakat, and they ran into the same issue again. In the third year, he sent him all of it, and Umar again argued with him. Mu’adh responded: “I could not find anyone who deserved to receive anything from me.” [Refer Al-Amwal]