When you send an email from your phone or computer, it isn't your email client that sends the email, it is sent by our server. If a customer responds to an email, you will get that response. If you wish to receive a copy of all emails sent you go to "Settings", "Company settings", "Email" and "Send me copies of all invoice emails" or "Send me copies of all quote emails".
When you look in the web service, the overview has the date when it was emailed. In the app you have a small blue envelope in the overview.
If you are working on an Android phone you can also choose to "Share". This will allow you to send the invoice or quote from your mail client. Any attachments will not be sent; it is only the invoice or quote that is shared.
If your customer tells you that they haven't received an email, check that the email address is correct, that you haven't received a bounce message and ask them to check their spam filter.