There are different ways to move email from one provider to another, even between email programs. Below we have two examples how you can do it.
Import function
Our webmail can import email from other email providers. You will need username password and imap server from your old provider. Notice that it is not 100% sure this method will work.
Email program
With your email program where you have your old email accound, you can add the new accound as IMAP-accound and "drag and drop" emails or folders from the old to the newly created one within the email program.