These are a few links I’ve used in working with migrating to Office 365:

1. Migrate all mailboxes to Exchange Online with a cutover migration
   • https://technet.microsoft.com/en-us/library/jj874016(v=exchg.150).aspx
2. Migrate Legacy Public Folders to Exchange Online Exchange 2013 Help
   • http://technet.microsoft.com/en-us/library/jj983799(v=exchg.150).aspx
3. Office 365 Identity Management with DirSync without Exchange Server On-Premises
   • http://blog.baeke.info/2012/06/24/office-365-identity-management-with-dirsync-without-exchange-server-on-premises/
4. Troubleshoot a hybrid deployment Exchange 2013 Help
   • https://technet.microsoft.com/en-us/library/jj659053(v=exchg.150).aspx
5. MessageOps – Exchange of O365 Welcome
   • http://www.messageops.com/documentation/office-365-documentation/office-365-end-user-training
6. Mailboxes 25 MB
   • http://www.linkedin.com/groups/Office-365-has-file-size-3724282.S.97439678