PHP-so sends links to gmail emails

Question

I have the following code that sends a password reset link, but the problem here is that if the email requesting a new password is gmail.com sends without any problem but if it is another email like Hotmail.com etc. simply does not send any link.

<?php
 include("config.php");
if(isset($_POST['submit_email']) && isset($_POST['email'])) {
    $email = mysqli_real_escape_string($conn, $_POST['email']);
    $sql = "SELECT * FROM registo WHERE email = '$email'";
    $r = mysqli_query($conn, $sql);
    $count = mysqli_num_rows($r);
    if($count == 1) {
        // Create new hash
        $key = hash('sha256', uniqid("", true));
        // SQL query to update user record with hash value
        $usql = "UPDATE registo set reset_key = '".$key."' where email = '".$email."'";
        if(!mysqli_query($conn, $usql)) {
            $message1 = "Error updating database!";
                echo "<script>alert('$message1'); window.location.href='reset.html';</script>";
            die();
        }
        // send link to user with generated key
        $link="<a href='http://unn-w17015779.newnumyspace.co.uk/reset.php?key=".$key."'>Click To Reset password</a>";
        $to = $email;
        $subject = 'Reset Password';
        $message = 'Click On This Link to Reset Password '.$link;
        $headers = 'From: Galaxy books shop <**@gmail.com>' . "\r\n" .
                   'Reply-To: **@gmail.com' . "\r\n" .
                   'X-Mailer: PHP/' . phpversion();
        // Send email
        if(mail($to, $subject, $message, $headers)){
            $message2 = "Your reset link has been sent to your email!";
                echo "<script>alert('$message2'); window.location.href='home.php';</script>";
        }else{
             $message3 = "Failed to Recover your password, try again!";
                echo "<script>alert('$message3'); window.location.href='reset.html';</script>";
        }
    } else {
        $message4 = "User name does not exist!";
                echo "<script>alert('$message4'); window.location.href='signup.html';</script>";
    }
}
?>