The benefit of moving to Microsoft's online servers, instead of e-mails going through e-mail servers at Lund University, is that we get access to better monitoring and management systems for malicious e-mails. As a user, you will not notice any difference, except that the text ***SPAM*** will no longer be in the subject line as previously on some e-mails. The hope is that the number of spams will decrease significantly with the new solution.
One of the major changes is that we will have access to a "quarantine" where everyone can look at malicious e-mails and possibly release them after self-monitoring. For more information on how to do this, see this article at LU-Service (in Swedish).
Always start by checking the list of "Blocked Senders" under Junk E-mail Options in your Outlook if you are missing an e-mail from a sender.