foobar.module

/**
 * Implements hook_theme_suggestions_hook_alter().
 */
function foobar_theme_suggestions_swiftmailer_alter(array &$suggestions, array $variables) {
  $module_defined = array_key_exists('module', $variables['message']);
  $key_defined    = array_key_exists('key', $variables['message']);
  if($module_defined && $key_defined) {
    $suggestions[] = 'swiftmailer__' . $variables['message']['module'];
    $suggestions[] = 'swiftmailer__' . $variables['message']['module'] . '__' . $variables['message']['key'];
  }
}

swiftmailer--example--recommend_mail.html.twig

{% extends "@my_theme/mail/swiftmailer.html.twig" %}

{% block body %}

  <h2>Hallo {{ recipient_name }}!</h2>
  <p>{{ sender_name }} ({{ sender_email }}) möchte Ihnen eine Seite im Intranet empfehlen:</p>
  <p><a href="{{ page_url }}">{{ page_title }}</a></p>
  {% if (message) %}
  <p>Darüber hinaus wurde folgende Nachricht hinterlassen:</p>
  <p style="font-weight: bold;">{{ message }}</p>
  <br />
  {% endif %}

  <p>Ihr Intranet-Team</p>

{% endblock %}

swiftmailer.html.twig

<?php
/**
 * @file
 * The default template file for e-mails.
 */
?>
<style type="text/css">
table tr td {
  font-family: Arial;
  font-size: 12px;
}
</style>

<div>
  <table width="800px" cellpadding="0" cellspacing="0">
    <tr>
      <td>
        <div style="padding: 0px 0px 0px 0px;">
          {{ body }}
        </div>
      </td>
    </tr>
  </table>
  
  <h1>My Awesome E-Mail Footer</h1>
</div>