RalfHermsen stukey OK - we also found setting the following DWORD to 1 can help with already-logged-in Skype for Business switching over to modern-authentication:
HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\15.0\Lync\ AllowAdalForNonLyncIndependentOfLync
HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\16.0\Lync\ AllowAdalForNonLyncIndependentOfLync
We also found setting this DWORD to 1 helps in the same way for Exchange Online, just in case:
HKEY_CURRENT_USER\Software\Microsoft\Exchange\AlwaysUseMSOAuthForAutoDiscover
https://docs.microsoft.com/ms-my/exchange/troubleshoot/modern-authentication/modern-authentication-configuration
https://support.microsoft.com/en-gb/help/3126599/outlook-prompts-for-password-when-modern-authentication-is-enabled