When we are looking for transitioning customer organization from third party messaging solution (non-Exchange system) such as Lotus Notes, Novel Netware, and Google to Microsoft Office 365, typically we need to follow the IMAP migration path. To avoid the any issues during a migration can be difficulty to people unfamiliar with the matter.
Microsoft released a new guide to IMAP migration troubleshooting tools. IMAP migrations provide organizations with an effective way to move email from any environment that support the IMAP protocol. This will used for any non-exchange source email system. If Exchange is the source you would likely opt for the Staged, Cutover, or Hybrid migration path.
Click here for IMAP Migration Troubleshooter
If you are looking for assistance on any troubleshooting Hybrid migrations click on Exchange Online Migration Guide