The PDF Invoices add-on allows you to issue invoices in PDF format and attach such invoices to messages.
The add-on places the "Open PDF invoice" button on the order confirmation page a customer sees after placing an order and the order details page that a customer can view in their account in the storefront's Orders section:
Order confirmation page
Order details page
A store admin also gets such a button on the order details page in the store's Admin area: