When dealing with attributes synced to O365 via FIM \ DirSync \ AAD Sync, you will frequently encounter the msExchRemoteRecipient type attribute, previously empty in on-prem Exchange (only msExchRecipientTypeDetails and msExchRecipientDisplayType had values) the msExchRemoteRecipientType will have the following values depending on the object type and how the mailbox and archive were enabled \ moved to O365....
msExchRemoteRecipientType:
3 ProvisionedMailbox, ProvisionedArchive (mailbox provisioned in Cloud & Archive provisioned in Cloud)* either via EMC or new-remotemailbox cmd
4 Migrated mailbox from on-prem
6 Migrated mailbox from on-prem, ProvisionedArchive in EXO (mailbox migrated from on-prem & archive provisioned in Cloud)
20 DeprovisionArchive, Migrated
100 Shared Mailbox in EXO
* A big THANKS to Lou Mandich (http://blogs.technet.com/b/loum/) for helping me round up the missing #6 ...