A common way a purchasing department works is to issue a purchase order which specifies what they want to purchase. An important feature of the purchase order is it has a unique ID. The purchasing department use this ID to track deliveries and payments. In particular the purchasing department always require the purchase order ID to specified on the invoice.
Therefore, if a purchasing department employs purchase orders the right procedure is follows:
the customer asks for quote,
based on the quote the customer issues a purchase order and ships that to the seller, and
finally, based on the purchase order the seller issues an invoice that shows the right purchase order ID.