Here are your options as I perceive:
1) To be able create a record in P/L Form Maintenance, have options for Print / PDF, Electronic Delivery / PDF All and similar, and have an entry appear in the Customer Viewer, you need a mod.
2) Manually Print to PDF at the time of Packing List printing. Save the PDF file name with the OrderNo or ShippingNo/InvoiceNo in it. Then create a ChilkatMail VB script to send an email with the PDF attached. The filename format allows finding the right PDF and finding the recipient email address from data entry. Chilkat is the 3rd party email program used by Paperless. @DanBurleson is good at stuff like this. He may have another idea.
3) Use K-Sync like it's been suggested here.
Personally I would format an invoice as a packing list.