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 enabled 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


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 


Set-CsOAuthConfiguration -ClientAdalAuthOverride Disallowed


Set-CsOAuthConfiguration -ClientAuthorizationOAuthServerIdentity ""

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