Stealth Redirection of website from another website (Third Party)

I thought you meant the content of example.google.com formed part of the content of , but now it seems it's the full site.

You can set up a dedicated vs to pass all traffic to example.google.com, but you should want to rewrite the request "Host:" header to "example.google.com":

when HTTP_REQUEST {
    HTTP:header replace Host "example.google.com"
}

You probably will also need to get your routing right to make this work.