I use Outlook 2016 in conjunction with Google Apps Sync for my email. I created a rule in Outlook that looks for text in the message header of the email that was BCC'd to me from Realvolve.
With this rule in place when I send email from Realvolve, Outlook automatically moves the email to the sent items folder as if I originated the email from Outlook. I believe you can do rules in Gmail, Yahoo, Office365, etc too.
* When the RV user goes to the message in Outlook and chooses FILE > PROPERTIES it shows the Header information inside that email message. Each Email has this "Header" information which gives the details of where it came from and server information that it traveled through.
Inside that "Header" is a section called "Return-Path" which is used when your server receives the email but some error prevented it from delivering it to your account, the server can send a message back through this "Return-Path" in the form of a "Bounced" message.
The RV user is using that "Return-Path" to find the unique mailbox that is your Realvolve account so it does not try and put other emails into the sent folder which are not from Realvolve.
* We recently changed some email settings which may require you to update your rule on this. It may be just fine but wanted to give you the heads up. We changed the email authority to help eliminate email bounces from some Email servers so just double check it. (8-4-16)