when message is sent fep_action_message_after_send is fired. first argument is message id of newly created message.

If you want to show only one message then you have to custom code for that. You can use fep_get_message_with_replies() function to retrieve any message and show them anywhere.

three arguments are sent from fep_action_message_after_send action.
You can use fep_get_message_with_replies( $id ) to get message with replies of given id.
Please see functions.php of this plugin to see code.

When you are getting your ID (from web app)? If you can capture your ID when message sent you can add like bellow code

add_action( 'fep_action_message_after_send', function( $message_id, $message, $inserted_message ){
    add_post_meta( $message_id, '_your_custom_meta_key', $id_from_web_app );
}, 10, 3 );

You can use $_SERVER['HTTP_REFERER'] to capture id or create a hidden field to provide that id. If you need more secure way you can create 2 hidden field, one for id and another for token created for that id. So that if anybody change that id, that will mismatch token so that you can reject that.

That will not be practical because every field require individual type of validation and sanitize.

You can easily capture id from url and add that in post meta. Use code like

add_action( 'fep_action_message_after_send', function( $message_id, $message, $inserted_message ){
    wp_parse_str( $_SERVER['HTTP_REFERER'], $referrer );
    $id = !empty( $referrer['id'] ) ? absint($referrer['id']) : 0; //Change id with your parameter
    //here if require check some validation
    add_post_meta( $message_id, '_your_custom_meta_key', $id );
}, 10, 3 );