Create PDF file from html ajax form in php

I have a simple contact form. It sends email via AJAX. Works fine.

Now I need to create PDF file from results of this form and download it to user like here

So html form:

<form id="contact-form">
    <input type="hidden" name="action" value="contact_send" />
    <input type="text" name="name" placeholder="Your name..." />
    <input type="email" name="email" placeholder="Your email..." />
    <textarea name="message" placeholder="Your message..."></textarea>
    <input type="submit" value="Send Message" />
</form>

In functions.php I have function to send email:

function sendContactFormToSiteAdmin () {

  try {
    if (empty($_POST['name']) || empty($_POST['email']) || empty($_POST['message'])) {
      throw new Exception('Bad form parameters. Check the markup to make sure you are naming the inputs correctly.');
    }
    if (!is_email($_POST['email'])) {
      throw new Exception('Email address not formatted correctly.');
    }

    $subject = 'Contact Form: '.$reason.' - '.$_POST['name'];
    $headers = 'From: My Blog Contact Form <contact@myblog.com>';
    $send_to = "contact@myblog.com";
    $subject = "MyBlog Contact Form ($reason): ".$_POST['name'];
    $message = "Message from ".$_POST['name'].": \n\n ". $_POST['message'] . " \n\n Reply to: " . $_POST['email'];

    if (wp_mail($send_to, $subject, $message, $headers)) {
      echo json_encode(array('status' => 'success', 'message' => 'Contact message sent.'));
      exit;
    } else {
      throw new Exception('Failed to send email. Check AJAX handler.');
    }
  } catch (Exception $e) {
    echo json_encode(array('status' => 'error', 'message' => $e->getMessage()));
    exit;
  }


}
add_action("wp_ajax_contact_send", "sendContactFormToSiteAdmin");
add_action("wp_ajax_nopriv_contact_send", "sendContactFormToSiteAdmin");

So in footer.php i have a script ajax handler:

jQuery(document).ready(function ($) {
    $('#contact-form').submit(function (e) {
      e.preventDefault(); // Prevent the default form submit
      var $this = $(this); // Cache this
      $.ajax({
        url: '<?php echo admin_url("admin-ajax.php") ?>', // Let WordPress figure this url out...
        type: 'post',
        dataType: 'JSON', // Set this so we don't need to decode the response...
        data: $this.serialize(), // One-liner form data prep...
        beforeSend: function () {},
        error: handleFormError,
        success: function (data) {
          if (data.status === 'success') {
           handleFormSuccess();
          } else {
            handleFormError(); // If we don't get the expected response, it's an error...
          }
        }
      });
    });
});

All of it works great. But i don't understand where i have to paste code for creation PDF, i have tried to paste it in sendContactFormToSiteAdmin php function, but it didn't work.

As in this example i need to paste this code exactly in sendContactFormToSiteAdmin php function:

ob_start();
?>

<h1>Data from form</h1>
<p>Name: <?php echo $name;?></p>
<p>Email: <?php echo $email;?></p>

<?php 
$body = ob_get_clean();
$body = iconv("UTF-8","UTF-8//IGNORE",$body);
include("mpdf/mpdf.php");
$mpdf=new \mPDF('c','A4','','' , 0, 0, 0, 0, 0, 0); 
$mpdf->WriteHTML($body);
$mpdf->Output('demo.pdf','D');

But i don't understand how to do this with ajax response.

Edit As Shoaib Zafar commented, if it is possible to email pdf file as an attachment to email, of course for me it is the best.