I have a customer who sells PDF's, and is asking if it possible that if PDF's can be sent to an online printing company and then the printed document will be sent directly from that printing company? All of this should happen without any involvement from the site owner.
I guess you should provide more insights to your solution partner but I guess is possible.
It will depend on some business rules and scnearios but it should be possible.
If you could be able to get the invoice for the PDF the customer has seelcted you can send (after the invoice is created) the PDF to your provider with the shipping information (remember to be sure about laws and shared information).
(my 2 cents)