We have a scheduled database task that calls the Email Customer Statements task and uses the parameters of Company and a Template.  You could have them emailed to a central mailbox using a similar process if you need intervention before someone then forwards on to the customer.

We only send them once a month.

You can schedule the report and use a report rule with “Route to connect” action to send the PDF to connect senders to store. Another option would be to use the report rule to set the printer as “SEND_TO_CONNECT” and then create a routing rule to catch this application message and set a particular routing address to save the PDF to any location that you want.