@old2 -- after you terminate the Shaw services, Shaw keeps your E-mail valid for a while, especially if you have Shaw hardware to return (or not return, and "buy" the equipment from Shaw). Shaw will put a $400 fee onto your account, until they receive the equipment you have returned. Then, Shaw will reverse the charge. After that, Shaw will terminate your access to your Shaw messages.
It seems that the onus is on you to use POP (Post Office Protocol) to download all your messages to your computer, before the termination of your access. I doubt that Shaw will tell you to use POP within an E-mail client -- just something not covered in the training of their employees.
