Mailer Form (Not Kirupa's)

Does anyone see anything with my code that would prevent certain user’s submissions from making it to the mailbox?

I am testing it and getting success, but my client keeps yelling at me because apparently he is being contacted by friends who are using it and not getting an email sent.

The form:

<form name="thisform" id="thisform" method="post" action="thank-you.php">
                <table>
                    <tr>
                        <td class="form_title">Name:</td>
                        <td class="form_form">
                            <input type="text" name="fullname" id="fullname" size="24" />
                        </td>
                    </tr>
                    <tr>
                        <td class="form_title">Email Address:</td>
                        <td class="form_form">
                            <input type="text" name="email" id="email" size="24" />
                        </td>
                    </tr>
                    <tr>
                        <td class="form_title">Phone (optional):</td>
                        <td class="form_form">
                            <input type="text" name="phone" id="phone" size="24" />
                        </td>
                    </tr>
                    <tr>
                        <td class="form_title"></td>
                        <td class="form_form">
                            <a href="#submit" id="submit_button"><img src="assets/images/submit.png" alt="submit"/></a>
                        </td>
                    </tr>
                </table>
                <input type="hidden" name="submitted" value="true"/>
            </form>

Javascript to Submit:

$(document).ready(function() { 
    $('#submit_button').click(function() {
    
        var fullname = $('input#fullname').val();
        var email = $('input#email').val();
        
        if(fullname == '' || email == '') {
            
            if(fullname == '') {
                $('#fullname').css('border', '2px solid #8cc63f');
            }
            if(email == '') {
                $('#email').css('border', '2px solid #8cc63f');
            }
            
            alert("Please complete all required fields.");
            
            return false;
        } else {
                document.thisform.submit();
        }
    });

});
</script>

Mail script on thank-you.php:

<?php
    if(isset($_POST['submitted'])) {
        $fullname = $_POST['fullname'];
        $email = $_POST['email'];
        $phone = $_POST['phone'];
        
        $subject = "Website Information";
        
        $message = "<p>The following message has been sent using the form on the Website:</p>
        <p>Name:<br>
         $fullname</p>
        <p>Email:<br>
         $email</p>
         <p>Phone:<br>
         $phone</p>
        ";
                
        // Mail of sender
        $mail_from="$email";
        // From:
        $header  = "MIME-Version: 1.0"."
";
        $header .= "Content-type: text/html; charset=utf-8"."
";
        $header .= "Content-Transfer-Encoding: 8bit"."
";
        $header .= "from: $fullname <$mail_from>";
                
        $send_contact=mail('my-email@gmail.com',$subject,$message);
    }

?>

Names have been changed to protect the innocent.

Thanks in advance.