Generate and send ICS file through WordPress

I'm writing a custom plugin for reservations. I need to generate an .ics file that needs to be sent to a predefined email address.

I've tried some library like ZContent iCalendar and a PHP script that I found on github that I've included inside my plugin code. The script works well and I can obtain a valid output. The problem is I can't figure out how to generate the ics file and attach it to an email using the wp_mail function.

Here is my code:

?php
/**
 * ICS.php
 * =======
 * Use this class to create an .ics file.
 *
 * Usage
 * -----
 * Basic usage - generate ics file contents (see below for available properties):
 *   $ics = new ICS($props);
 *   $ics_file_contents = $ics-to_string();
 *
 * Setting properties after instantiation
 *   $ics = new ICS();
 *   $ics-set('summary', 'My awesome event');
 *
 * You can also set multiple properties at the same time by using an array:
 *   $ics-set(array(
 *     'dtstart' = 'now + 30 minutes',
 *     'dtend' = 'now + 1 hour'
 *   ));
 *
 * Available properties
 * --------------------
 * description
 *   String description of the event.
 * dtend
 *   A date/time stamp designating the end of the event. You can use either a
 *   DateTime object or a PHP datetime format string (e.g. "now + 1 hour").
 * dtstart
 *   A date/time stamp designating the start of the event. You can use either a
 *   DateTime object or a PHP datetime format string (e.g. "now + 1 hour").
 * location
 *   String address or description of the location of the event.
 * summary
 *   String short summary of the event - usually used as the title.
 * url
 *   A url to attach to the the event. Make sure to add the protocol (http://
 *   or https://).
 */
class WP_ICS{
  const DT_FORMAT = 'Ymd\THis\Z';
  protected $properties = array();
  private $available_properties = array(
    'description',
    'dtend',
    'dtstart',
    'location',
    'summary',
    'url'
  );
  public function __construct($props) {
    $this-set($props);
  }
  public function set($key, $val = false) {
    if (is_array($key)) {
      foreach ($key as $k = $v) {
        $this-set($k, $v);
      }
    } else {
      if (in_array($key, $this-available_properties)) {
        $this-properties[$key] = $this-sanitize_val($val, $key);
      }
    }
  }
  public function to_string() {
    $rows = $this-build_props();
    return implode("\r\n", $rows);
  }
  private function build_props() {
    // Build ICS properties - add header
    $ics_props = array(
      'BEGIN:VCALENDAR',
      'VERSION:2.0',
      'PRODID:-//hacksw/handcal//NONSGML v1.0//EN',
      'CALSCALE:GREGORIAN',
      'BEGIN:VEVENT'
    );
    // Build ICS properties - add header
    $props = array();
    foreach($this-properties as $k = $v) {
      $props[strtoupper($k . ($k === 'url' ? ';VALUE=URI' : ''))] = $v;
    }
    // Set some default values
    $props['DTSTAMP'] = $this-format_timestamp('now');
    $props['UID'] = uniqid();
    // Append properties
    foreach ($props as $k = $v) {
      $ics_props[] = "$k:$v";
    }
    // Build ICS properties - add footer
    $ics_props[] = 'END:VEVENT';
    $ics_props[] = 'END:VCALENDAR';
    return $ics_props;
  }
  private function sanitize_val($val, $key = false) {
    switch($key) {
      case 'dtend':
      case 'dtstamp':
      case 'dtstart':
        $val = $this-format_timestamp($val);
        break;
      default:
        $val = $this-escape_string($val);
    }
    return $val;
  }
  private function format_timestamp($timestamp) {
    $dt = new DateTime($timestamp);
    return $dt-format(self::DT_FORMAT);
  }
  private function escape_string($str) {
    return preg_replace('/([\,;])/','\\\$1', $str);
  }
}


class iCalBooking{

  public function init(){
    add_action('admin_post_forward_booking_request', array($this, 'send_booking_request'));
    add_action('admin_post_nopriv_forward_booking_request', array($this, 'send_booking_request'));
    #add_action();
    add_shortcode('booking', array($this, 'display_booking_form'));
  }

  public function display_booking_form(){
    include_once 'booking-form.php';
  }

  private function has_valid_nonce() {
      if(!isset( $_POST['booking_nonce'] )){
        return false;
      }
      $field  = wp_unslash( $_POST['booking_nonce'] );
      $action = 'validate_booking_request';
      return wp_verify_nonce( $field, $action );
  }

  public function send_booking_request(){
    if(! ( $this-has_valid_nonce() ) ){
      return;
    }
    $fname = $_POST['client_fname'];
    $lname = $_POST['client_lname'];
    $phone = $_POS['client_phone'];
    $email = $_POST['client_email'];

    $title = 'Prenotazione';

    $description = $fname . $lname . $phone . $email;


    $ics = new WP_ICS(array(
      'location' = '',
      'description' = $description,
      'dtstart' = $_POST['client_checkin'],
      'dtend' = $_POST['client_checkout'],
      'summary' = '',
      'url' = ''
    ));

    file_put_contents('reservation.ics', $ics-to_string() );

    #header('Content-Type: text/calendar; charset=utf-8');
    #header('Content-Disposition: attachment; filename=reservation.ics');


  }

}

$booking = new iCalBooking;
$booking-init();
?