Hey there! This sounds like an issue with the Outlook side of things and not the server side. If Outlook is repeatedly sending the message the mailserver will just listen and deliver the message as best it can, but Exim won't deliver a message multiple times.
You could confirm this is the case by searching the /var/log/exim_mainlog file on the system for the subject line of the duplicate messages. If there are multiple mail IDs with that same subject, the server side received the message twice.
It might be good to check the user's login details in /var/log/maillog to see if there are any authentication issues causing this. It may also be a good idea to try sending a message from the user's webmail to see if that works properly, as that may reveal some errors directly in the interface if something is wrong.
