The new article titled New solution for: Riva put sent items into Inbox, after sync with CRM supersedes this article, number 435. (Article number 435 is no longer being maintained.)
By default, Riva moves outbound email from Riva email drop folders back to the Sent Items folder after the email item has been synced to the CRM.
Riva has sometimes moved outbound email to the Inbox instead of the Sent Items folder after the email had been synced to the CRM.
Riva had an issue with email sync against mailboxes hosted on some builds of Exchange 2013.
The solution that was offered in previous versions of this article did not work all the time.
For a solution that works all the time, see Knowledge Base article 1364.