Moodle forums don't integrate email bidirectional. This is, email responses to forum posts don't appear on the Moodle forums. The answer from an email user's account is only sent to the person who wrote the post. We need that this answer appear also in the Moodle forum where were wrote the post.

I'm not sure if this option is avalaible in the latest versions of Moodle. I've done a process.php to try resolve that question. Do you think that it could be an interesting option?