If the option to Connect as is greyed out in the Map Network Drive group policy preference, you can fix this by uninstalling a Windows patch. To enable Connect as in the Map Network Drive group policy preference, uninstall patch MS15 015.
This was implemented by Microsoft as they decided that the ability to store passwords in Active Directory group policy is not secure – indeed, any user that the policy applies to can just navigate to the policy in the sysvol share and read the username and password from the Map Network Drive group policy.
What’s the big problem with users getting access to a password that gives them access to things they already have access to, you might be wondering? Well, it’s a problem because the user could then log on to other services (or their computer) with the username / password combination and then become untraceable.
My recommendation is that instead of saving credentials in the Connect as part of the Map Network Drive GPO Preference, that you should implement correct security group permissions on the shared drive you are connecting the user to.