If Skype for business is prompting for a password via a web page via as seen below in a fashion duplicating that of the normal login.   What you are seeing is the result of Modern Authentication being enable in the Skype for Business Server.   





It is possible to disable modern authentication for Skype for Business either locally for the account via the registry with


Computer\HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Lync\<user@domain.com>\


DWORD  OAuthUsed  1


Change to 0 to disable.



Or globally,


Set-ExecutionPolicy RemoteSigned

# Connect to Skype For Business Online

# Install Skype For Business Online  PS Module
# https://www.microsoft.com/en-us/download/confirmation.aspx?id=39366

$credential = Get-Credential

Import-Module SkypeOnlineConnector

$sfboSession = New-CsOnlineSession -Credential $credential
Import-PSSession $sfboSession


For Skype for Business 


Online

Set-CsOAuthConfiguration -ClientAdalAuthOverride Disallowed


On-Premises

Set-CsOAuthConfiguration -ClientAuthorizationOAuthServerIdentity ""


Note: Server Updates can take time to be applied and are not immediate.