Some users are reporting a persistent password popup in their mail application this morning, this is due to Microsoft changing the Microsoft/Office 365 authentication method and requiring 'modern authentication' by default.
If you are using Outlook 2013 this can easily be solved by changing\adding a Registry setting in Windows which is normal and 'IT support level' change:
This can also be easily pushed out by 'group policy' if you have a Windows domain.
If you're seeing this in another mail app for example on your phone this will require further investigation and planning.
Here is some further reading on the subject:
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Digitalwelcomemat provides IT consultancy and services for business customers on the NSW Central Coast in Australia.