Two points :
- It is useless to run WPP on the replica server. You will no be able to manage that server. Run WPP directly from your computer (Ensure the Wsus Console is installed).
- You don't have to be in the Windows Administrators group to manage a Wsus with WPP (or Wsus Console). You just have to use an account that is member of the "Wsus administrators" group, that is, is administrator of the Wsus functionality (not of Windows Server)
