Firstly, if you want to use Windows authentication, you need to configure your site to use Windows authentication, not Forms authentication.
Secondly, if you want the client to silently authenticate to your site, without prompting the user for a username and password, then the client needs to be a member of the same Active Directory domain as the server, and the site needs to be in the client's "Local Intranet" zone.
NB: Adding the site to the "Local Intranet" zone in the Internet Explorer settings will affect Internet Explorer, Edge, and Chrome. To get the same result in Firefox, you'll need to modify the configuration:
Enabling NTLM Authentication (Single Sign-On) in Firefox[
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