Once you have UPN suffixes configured to support the logins that you'll use in Office 365, you'll need to go into the Properties for each user, and ensure their UPN uses the correct domain suffix.
To do this, go to Active Directory Users and Computers, find the user and open properties. The domain suffix is under the Account tab:
Of course, this can be quite onerous if you have a lot of users, so you may want to use PowerShell to do this. Now, we'd be happy to show you, but our editors think this book is already too long, so please head over to Microsoft's Hey, Scripting Guy! blog and ...