How can I see if a customer's invoice has been uploaded?

To check if a customer's invoice, statement or other document has been uploaded, select 'Documents' on the top left and then 'Search & Compose' from the page you are brought to.  Then enter your search criteria (e.g. Invoice No, Account Code, or Account Name) and click 'Refresh'.

You will be presented with a list of recent documents, which allow you to see what has been sent most recently for that account.