Email forwarding guarantees that, even after terminating your service, emails will still be sent to your CenturyLink address. You can have all incoming emails automatically routed to a different email address of your choosing by configuring email forwarding: Here's how to get everything ready:
Open your CenturyLink webmail account and log in.
Locate the 'Mail Forwarding' settings under 'Settings'.
Type in the email address you wish to use for email forwarding.
Save the modifications and turn on forwarding.
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