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....
1 Provisioned User Mailbox
3 Provisioned User Mailbox, Provisioned Archive
4 Migrated User Mailbox
6 Migrated User Mailbox, Archive created in cloud
20 Migrated User Mailbox, deprovisioned Archive
33 Provisioned Room Mailbox
36 Migrated Room Mailbox
65 Provisioned Equipment Mailbox
68 Migrated Equipment Mailbox
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 ...