All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First, we beseech Allaah The Exalted in supplication to facilitate your affairs and grant you success. As for your inquiry, carrying out the engagement via correspondence is permissible, since the purpose of engagement is informing the girl’s family of your wish to marry her.
Allaah Knows best.