If I understand this question correctly. You are hosting a website, and the website makes a request to a PHP script that in turn calls an API that returns some set-cookie headers.

For the cookies to be passed on to the client viewing the website, you'd need to extract the cookie values and call PHPs setcookie function before returning the response to the client from PHP.

Most frameworks will provide a mechanism to specify the header for the response to the client and provide the ability to set a cookie.

Based on your update:

// Here is how I am calling the server 2 file.
$.ajax({
            URL:"HTTP://localhost......server.php",
            type:"post",
            data: $(this).serialize(),
            success: .....,
        });

So you have some JS that is making a request to the "server 2" file. This "server 2" file should be able to extract the values from the response to the curl call it is making and return set-cookie headers to the client. The client will then store those cookies and could provide them on subsequent requests to http://localhost, for how long, for what paths etc are configurable as part of the process for creating the cookie.

Might be worth posting more code, or making it clearer what you aim is with this as there may be a better solution outside of extracting cookie data from the curl call and passing back to the client.