Synching Mail Sent folder on new computer I have an iMac and a 2009 Mac Pro 4.1.  Both run OS X 10.11.3.  I recently used Migration Assistant to move data, applications, and settings from the iMac to the Mac Pro.  

I had some other problems that I had to get fixed with the Mac Pro before I could make it my primary desktop machine.  The problems took several days to get solved.  

Because of this situation, the Mail Sent folder has gotten out of sync on the two machines.  While all incoming mail shows up on the Mac Pro, none of the email Sent (to others) from the iMac shows up on the Mac Pro. 

As my Sent mail serves as a useful resource, does anyway exist for my Sent folders to synchronize (other than sending my self every mail that I've sent over the days from the iMac)?
Have you checked that the "Sent option" is correctly enabled in your devices?
In iMac: 


Open Preferences > Account;
Select your account;
Press the "Mailbox behaviour" tab;
Make sure the "Store sent messages on the server" option is enabled. In this way, sent messages will be stored on the server, and will downloaded in all your devices.