The Microsoft Remote Connectivity Analyzer was just released. This helps troubleshoot Office 365 Connection Problems and includes an Office 365 Connectivity Analyzer for federated sign-on and many other Exchange Online integration features.
You can check out the Microsoft Remote Connectivity Analyzer here: https://www.testexchangeconnectivity.com/.
For hotline support regarding your Office 365 connection problem, please feel free to call 1-855-IT-BOOST
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