Email migration issue

Job ID: 35576807

Budget: $10 – $30 USD

I was moving a site/email to a new server, and exported all of the old email. However, when I created new accounts (on the new server) the email on my computer would not "push up" and populate the accounts.
The accounts are receiving email - everything is connected - but I can't seem to get the old mail onto the accounts.
No - I cannot FTP them up - the server (Siteground) does not allow that level of servers access - they will have to go up using a mail client or something like that.
Please do not respond unless you understand that and have a solution that does not involve FTP.
Related categories: PHP System Admin Linux DNS Email Handling