Once a customer accepts a quote, open it in your dashboard and choose Convert to invoice. Everything carries across - the customer, the lines of work, the prices and VAT, the design - and the new document takes the next invoice number in your sequence. The quote stays in your records, linked to the invoice it became.
Edit the invoice before sending if the job changed: add a line, adjust a price, set the due date. Then send it or download the PDF as usual.
This is also how a proforma invoice works in FullDiary: the quote is the priced, dated document you send for approval or a deposit, and the real invoice follows from it in one click.