Probably this issue:
For More Information see: Send Mail using Outlook 2010 Error
This is one of many acknowledged bugs that can be found in the Known Bug List thread here in the Report an Issue section of the forum.
It can also be downloaded as a database file from: https://www.dropbox.com/s/jt09b82i0xijbu3/FMP%20Bugs.zip
Issue is with Outlook 2013. Outlook 2010 worked just fine. This reference is not the problem.
There are no error messages - the email just doesn't get sent or show up anywhere.
I downloaded and searched the 'Bugs' database referenced above for Outlook 2013 and found nothing.
I offered the user a work-around by using 'Send Via' 'SMTP Server'. Since they wanted a copy of the message in Outlook they have to 'bcc' themselves on every email. Their record of the email now appears in their Outlook 'in' box, not their 'sent' folder.
It would be better if an Outlook solution could be found.
Newer versions of outlook are to my understanding 64 bit.
You are welcome to post your own bug report over in Report an Issue if you'd like a TS technician to take a closer look at your issue.