With SSO, there is a federation trust relationship between Office365 and the onpremises AD FS, so the user logs on as user@lucernepublishing.com and that logon request is redirected to AD FS. AD FS constructs a token and passes that token to Office365. Office365 then grants the user access to his or her mailbox based on the fact that they were successfully authenticated by the onpremise ActiveDirectoryDirectoryService.
In the case of DirSync, Dirsync with password Sync, or AD FS (which is implemented with DirSync), there are additional ways to create email addresses and have those addresses replicate into Office365. To perform this procedure, complete the following steps: