Intuit won't allow us users to send via our own email clients, why I don't know but it's been a constant request for years. No idea why they won't, probably because they'd have to spend some money by the product development team.
The only way round it is to generate the invoice in QBO, hit save & send, you can then download the invoice as a PDF, save it to you computer and then send it via your normal email client. It's a very clunky method but not much else you can do. The invoice will be then saved as normal in QBO so when you get paid you can assign the payment to the invoice(s). You would need to do the same with statements, download as PDF and send via your email client.
