Need to track customers as paid in sales order fulfillment center.

Is there a way to track which customers have paid in the sales order fulfillment center? Inventory availability doesn't matter if they haven't paid.... I need to not only see that inventory is available, but also that the particular customer has paid so I can ship. Is there a way to do this? It doesn't make sense to run between invoices and the sales order center trying to remember which customer paid.