Can I keep a 0 quantity item on an invoice so it matches sales order?

We have a customer who requires the invoice lines to match the sales order lines, even if we can't fulfill an item due to a shortage.  For example, they order 5 different items on 5 different lines.  Lets call it product A, B, C, D and E.    We only have product to fulfill 4 of the lines.  We are out of product D.   In our normal practice, we would update the sales order to quantity of 0 and save the order.  When we do this, however, and after we fulfill the order, that line does not come to the invoice