Hi Tom,
As long as the user was authenticated at the time of paying the invoice, he can find the history of his paid ones by clicking the "My Account" link which goes to the user profile and the history will be under the Order History tab just like products purchased from webstore or ticket purchases from Event Calendar Pro, all ecommerce activity is listed there with links to the orders.
Are you sure you want them to be able to see cancelled invoices? I would not think I would want customers to see invoices I've created but cancelled.
Best,
Joe