Note: Following these steps will only work for email that is in one's Inbox. It will not export archived mail or mail inside folders.
In Gmail, go to Settings> Accounts and Import>Import Mail and Contacts> enter your firstname.lastname@example.org, enter your password, enter your account name>click Import
After setting up Gmail import users should set up a FC mailbox rule to auto-delete messages after a period of time.
You can easily set a mailbox rule to delete messages after a period of time.
~ Right-click your FC mailbox and choose "Rules"