OUTLOOK 365 - keeping same email addresses after crash

I have a client whose email account was infected.  Their email vendor has set them up on outlook 365 so they can continue service.  They were using Outlook for their old, infected account, but not through this 365 service.  Now they want to be able to keep their same email address and keep all their old emails that are currently stored locally.  Is there anything they have to do to be able to sync with new email and still keep their older email data online?