Add your account as IMAP, starting from File/New/Existing Mail Account, to download existing mail and folders. If you have an account already set up in another mail client, it can probably be imported to TB.

https://www.centurylink.com/home/help/internet/email/how-to-set-up-your-email-server-settings-to-go-through-pop-and-smtp.html

I'm sorry, but this wasn't a helpful solution. I don't want to do anything with Century Link anymore. That's why I was asking you how I can import my current existing Century Link email account and folders to TB. Then, you sent me a link to Century Link again. So, I need a solution to do it without contacting Century Link. Thanks!

If you're mail isn't currently stored on Centurylink servers, where are your 'existing emails and folders'? In some other mail app or in some format on the computer?