1. Have console connected to Xbox Live to update online gamertag profile. (May need to play and save game to update online gamertag profile or add any recent achievements) 2. Carefully transfer all save data to 2TB external drive. 3. Follow support link
http://support.xbox.com/en-US/xbox-360/accessories/add-remove-hard-drive to remove Internal HDD 4. Turn on console with external 2TB HDD connected, and without being logged into Xbox Live; Press Guide Button on controller, and download your gamertag profile
to external HDD. (Make sure your gamertag profile is working online, by checking to see if save data can be used on external HDD for games, as new System File should be created to external HDD) 5. Follow step 3 to install Internal HDD, and restart console
with external HDD connected. 6. Follow support link http://support.xbox.com/en-US/xbox-360/accessories/storage to format Internal HDD (You will need access to back of console for console serial number) Note: If, System File or Gamertag Profile is created to
Internal HDD, after format; Just delete them, after you confirm that they are safely stored to External HDD etc.
I couldn't say for certain on Xbox360: You May see slight performance benefit from using faster external HDD with latest Xbox360 dashboard update, and it will depend on the condition of your console and/or internal components.