Solution for checking the checkboxes with php. Think I must use a value

The checkboxes query works offline, but not online. I think I have to work with a value. It should not be a selection, but all checkboxes must be selected to be able to send.

I can not find the right solution in PHP. The checkboxes are checked but not processed.

Can somebody help me with the php-code?

<form id="contact-form" action="#">

  <div class="row contact-row">
    <div class="col-md-6 col-sm-6 col-xs-6 contact-name">
      <input type="text" id="firstname" name="firstname" placeholder="Vorname" required>
    </div>
    <div class="col-md-6 col-sm-6 col-xs-6 contact-name">
      <input type="text" id="lastname" name="lastname" placeholder="Nachname" required>
    </div>
  </div>

  <div class="row contact-row">
    <div class="col-md-6 col-sm-6 col-xs-6 contact-name">
      <input name="telefon" id="telefon" type="text" placeholder="Telefon" required>
    </div>
    <div class="col-md-6 col-sm-6 col-xs-6 contact-email">
      <input name="email" id="email" type="email" placeholder="E-mail" required>
    </div>
  </div>

  <input name="subject" id="subject" type="text" placeholder="Anfrage zur Immobilie 2018_1400">
  <textarea name="message" id="message" placeholder="Nachricht" rows="5"></textarea>

  <div class="col-md-12 col-sm-12 col-xs-12 mb-30">
    <h6>Your Choose</h6>
    <ul class="checkboxes">
      <li>
        <input type="checkbox" class="input-checkbox" name="checkbox1" id="checkbox1" required>
        <label for="checkbox1">*&nbsp;&nbsp;Red</label>
      </li>
      <li>
        <input type="checkbox" class="input-checkbox" name="checkbox2" id="checkbox2" required>
        <label for="checkbox2">*&nbsp;&nbsp;White </label>
      </li>
      <li>
        <input type="checkbox" class="input-checkbox" name="checkbox3" id="checkbox3" required>
        <label for="checkbox3">*&nbsp;&nbsp;Blue</label>
      </li>
    </ul>
  </div>

  <input type="submit" class="btn btn-lg btn-color btn-submit" value="Nachricht senden" id="submit-message">
  <div id="msg" class="message"></div>
</form>

<?php
if ($_POST) {

    $to = "abcd.de"; // email here
    $subject = 'Kontaktformular '; // Subject message here

}

//Send mail function
function send_mail($to, $subject, $message, $headers)
{
    if (@mail($to, $subject, $message, $headers)) {
        echo json_encode(array('info' => 'success', 'msg' => "Message send. "));
    } else {
        echo json_encode(array('info' => 'error', 'msg' => "Message not send."));
    }
}

//Check if $_POST vars are set
if (!isset($_POST['firstname']) || !isset($_POST['lastname']) || !isset($_POST['telefon']) || !isset($_POST['email']) || !isset($_POST['message'])) {
    echo json_encode(array('info' => 'error', 'msg' => 'Fill out all fields.'));
}


//Sanitize input data, remove all illegal characters    
$firstname = filter_var($_POST['firstname'], FILTER_SANITIZE_STRING);
$lastname = filter_var($_POST['lastname'], FILTER_SANITIZE_STRING);

$telefon = filter_var($_POST['telefon'], FILTER_SANITIZE_STRING);
$email = filter_var($_POST['email'], FILTER_SANITIZE_EMAIL);

$website = filter_var($_POST['website'], FILTER_SANITIZE_STRING);
$message = filter_var($_POST['message'], FILTER_SANITIZE_STRING);


//Validation
if ($firstname == '') {
    echo json_encode(array('info' => 'error', 'msg' => "Firstname please."));
    exit();
}
if ($lastname == '') {
    echo json_encode(array('info' => 'error', 'msg' => "Lastname please."));
    exit();
}

if ($telefon == '') {
    echo json_encode(array('info' => 'error', 'msg' => "Telefon?"));
    exit();
}

if (!filter_var($email, FILTER_VALIDATE_EMAIL)) {
    echo json_encode(array('info' => 'error', 'msg' => "Valid e-mail."));
    exit();
}

if ($message == '') {
    echo json_encode(array('info' => 'error', 'msg' => "Message?"));
    exit();
}

if ($checkbox1 == '') {
    echo json_encode(array('info' => 'error', 'msg' => "choose 1."));
    exit();
}
if ($checkbox2 == '') {
    echo json_encode(array('info' => 'error', 'msg' => "choose 2."));
    exit();
}
if ($checkbox3 == '') {
    echo json_encode(array('info' => 'error', 'msg' => "choose 3."));
    exit();
}


//Send Mail
$headers = 'From: ' . $email . '' . "\r\n" .
    'Reply-To: ' . $email . '' . "\r\n" .
    'X-Mailer: PHP/' . phpversion();

send_mail($to, $subject, $message . "\r\n\n" . 'Vorname: ' . $firstname . "\r\n" . 'Nachname: ' . $lastname . "\r\n" . 'Telefon: ' . $telefon . "\r\n" . 'Email: ' . $email, $headers);
?>

(function($) {
  "use strict";
  var submitContact = $('#submit-message'),
    message = $('#msg');

  submitContact.on('click', function(e) {
    e.preventDefault();

    var $this = $(this);

    $.ajax({
      type: "POST",
      url: 'mail-send.php',
      dataType: 'json',
      cache: false,
      data: $('#contact-form').serialize(),
      success: function(data) {

        if (data.info !== 'error') {
          $this.parents('form').find('input[type=text],input[type=email],input[type=checkbox],textarea,select').filter(':visible').val('');
          message.hide().removeClass('success').removeClass('error').addClass('success').html(data.msg).fadeIn('slow').delay(5000).fadeOut('slow');
        } else {
          message.hide().removeClass('success').removeClass('error').addClass('error').html(data.msg).fadeIn('slow').delay(5000).fadeOut('slow');
        }
      }
    });
  });

});