Is it possible to set a cookie on another domain using javascript?

I’m trying to set a same cookie on a website A and a website B.
I’m using xhr to send a request from the website A to the website B.

Here’s the code that I use:

JS code from the website A:

var xhr = new XMLHttpRequest();
            xhr.open('GET', 'https://websiteb.com/?sessid=<?php echo session_id(); ?>', true);
            xhr.withCredentials = true;
            xhr.send(null);

PHP code from the website B:

header("Access-Control-Allow-Credentials: true");
header("Access-Control-Allow-Headers: Set-Cookie");
header("Access-Control-Allow-Origin: https://websiteA.tld");
header('Content-Type: application/json');
setcookie('PHPSESSID', $_GET['sessid'], array(
        'expires' => time() + $cookielifetime,
        'path' => '/',
        'secure' => true,
        'httponly' => false,
        'SameSite' => 'None'
));

From my home computer (using Google Chrome Canary) it works.
But from my laptop (and my friend’s laptop), the cookie’s not set.

I tried to send a postman post request to see if the cookie would be set, but I only get the website A’s cookie.

Postman POST Request

Is there somebody here that can help me (or can tell me how I can set a cookie on a different domain)?