Sometimes the iPhone or iPad won’t automatically detect the correct Sent Items IMAP folder on the server and will resort to storing Sent Items locally. Very annoying. Here is how to correct this on the iPhone – it’s very similar for the iPad.
Open the settings icon and then click on the problem email account.
Click on the Account button to edit the account settings.
Scroll right to the bottom and click on the Advanced button.
Click on the Sent Mailbox button
Click on the appropriate “Sent” folder under the On the Server section. You will probably see that the On My iPhone – Sent folder is currently set. Once you are done click in the top left to go back to the previous Advanced screen, then then again to return to the Account screen. Then, importantly, click the Done button to save the changes.