I believe that whatever you want is called Single Sign-On ( SSO), that is, the user's ability to perform authentication once, and from there, all systems share the login information.
On the web, authentication sharing is common across the OpenID standard. This is the case of "Login with Google" or "Login with Facebook" or "Login with Twitter" that many sites offer.
On intranets, it is very common for systems to perform SSO using the LDAP protocol in a Active Directory (Windows).
However, SSO does not always provide a transparent user login, that is, many implementations require the user to retype their credentials with each authentication.
I did a search for "php sso active directory transparent login" and got up to this post from the SO , through which I got up to this page about an Apache extension called mod_auth_kerb .
I'm not a network or Windows Server expert, but I'm already aware that deploying all the required infrastructure can be a very labor-intensive and complicated process.
Of course, you can do some other trick that simply takes the user name somewhere, but then the security goes down.