Communications (SMS and emails) to Clients are all logged, including invoices sent to them.
To access the list of messages/communications, in the left-hand-menu click on Clients > List then choose the Client you're interested in.
Clicking on their name will show you their details and in the left-hand-menu will display a sub-menu in which you'll see "Communication".
If an invoice has been sent to that Client you will see a red circle with a $ symbol in it. You will see the date sent plus the invoice number.
To cross reference invoice numbers I recommend having another tab open with the Invoices listed.