Patrick, a Shopify Guru here :).
At the moment, we don't have direct method of taking payments for a purchase order. That being said once you have received the PO and are ready to ship you can create a new order which would update your inventory and let the customer pay for the items. Have a look here for more info about create a draft order
Hope that helps :)
I think the question if for business to business users who accept Purchase Orders as the initial method of payment and extend credit to the customers, either Net 15, Net 30 or Net 45. This means that the PO would be the confirmation of the order and the payment would occur after delivery.
Paypal has this function that allows for the payment not to actually be processed until the item arrives at the customer.
Without this functionality we would not be able to use Shopify for a B2B.
The only workaround I can think of is creating a Quote and then executing the quote by using "Mark as Paid" but this isn't a great workaround unless you are using another system to receive payments in.
Check out our new Purchase Orders app here https://apps.shopify.com/purchase-orders-1
Hope this helps