If your previous emails are stored in your account, then they will be imported automatically. The IMAP protocol allows you to synchronize the folders and emails with the registered email server, Hence it allows you to manage and organize your emails on almost any gadget that is associated with your Yandex Mail account. The moment you add your Yandex.ru account to the official Mailbird, you will get access to your Yandex emails immediately. And the process would end. Note: emails from the local server are impossible to import because of IMAP server protocols.