Hi @Eduards , what's your on-premise server version and are you using Exchange hybrid?
According to your information, does the issue only occurs on one user?
If the account can login to OWA successfully, the issue maybe related to autodiscover. Have you tried creating a new outlook profile for that user?
We can also use the ExRCA tool to help check the issue through this link: Outlook Connectivity
You could also refer to the method introduced below if your scenario mathches with it:
Outlook prompts for password after migration to Office 365
If you are not using the latest version of Outlook, Outlook doesn’t use Modern Authentication to connect to Office 365.
Go to the path HKEY_CURRENT_USER\Software\Microsoft\Exchange. Add a new DWORD (32-bit) Value. Add the name AlwaysUseMSOAuthForAutoDiscover with the value data 1.
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