Hi Victor,
Thanks for clarifying this issue so clearly. I appreciate your time and patience in troubleshooting this issue. Based on my experience, this kind of issue could be caused by multiple reasons. After doing some analysis, I find the local environment is a bit complicated. May I know the following information for further troubleshooting?
1. You have an on-premise Exchange server, but hasn’t deployed Exchange hybrid. Have you done any integration between on-premise Exchange and Exchange Online? Are on-premise Exchange and Exchange Online separate Exchange systems?
2. Your federated domain is krypton-solutions.com, is this domain also used in your on-premise Exchange organization?
3. I find you have pointed the MX record to Office 365 mail server, have you configured the Autodiscover record?
4. How do you configure the Exchange Online account in Outlook client, via POP/IMAP or configuring the account automatically via Autodiscover service?
If I have missed any points, please feel free to correct me and provide detailed information of the local environment. This will be very useful to analyze this problem. After confirming the information above, we will help you do some further investigation. Moreover, have you tried to run Desktop Setup for Outlook 2007/2010 users, and remove the cached credential as I mentioned above?
Thanks,
Young Yang