If a quote is created within ESC and the customer accepts the quote, you definitely want to make sure that the resulting invoices is tied back to that quote to make sure the quote gets marked as 'Billed'. One way to accomplish this would be to open the quote itself and click the Bill button on the toolbar. You may then select Convert Quote Into Invoice to carry all of the information and items from the quote into an invoice.
The Bill button on the Quote toolbar also has a Progressive Bill option which allows you to break the quote into multiple invoices. This is called Progressive Billing and allows the customer to pay off a large amount in phases or partial payments.
Another great way to ensure your quote gets billed properly is to dispatch it. Once the customer accepts the quote, you'll want to open the quote on the screen and go to Activities → Create Dispatch. This will give you the opportunity to carry the items on the quote to the dispatch. When the dispatch is completed and invoiced, the quote will be marked as billed.