Написал в грузинское консульство. Получил вот такой авто-ответ:
For immigrant visa (IV) cases (including diversity visa and K visa cases):
· IV services are currently available only to citizens and current residents of Georgia and Azerbaijan.
· We are not able to accept transfer requests for cases assigned to other embassies or consulates except for citizens and current residents of Georgian and Azerbaijan. If your email is a case transfer request, and you are not a citizen or current resident of Georgia or Azerbaijan, you will not receive a response.