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Assuming you are using IMAP, you can Sync Sent Messages by following these instructions per device:
Note: The IMAP Path Prefix should normally be set to INBOX

iPhone:

1) On your iPhone, go to settings.
2) Select Mail Contacts and Calendars
3) Select the account you are having problems with.
4) Go to the Advanced section at the bottom
5) Located in the Mailbox Behaviors section, click Sent Mailbox
6) Make sure that the folder “Sent” is enabled in the “On the Server” section

Outlook 2010:

1) Open your IMAP account settings via; File-> Account Settings-> Account Settings…-> double click on the IMAP account.
2) Press the button: More Settings…
3) Select the Sent Items tab.
4) Enable the option “Save sent items in the following folder on the server”.
5) Select the folder where you want to store the Sent Items in. (Sent)
You can press More Folders… if you do not see all your IMAP folders in the list. 

If outlook is not syncing the mail, check to see what is specified in the 'Root Folder Path' area found in Advanced settings