You can use following code, it will redirect user to messagebox page after message sent.
add_action( 'fep_posted_action_after', function( $action ){
if ( 'newmessage' == $action && count( fep_success()->get_error_messages() ) > 0 ) {
$_POST['fep_redirect'] = fep_query_url( 'messagebox' );
}
});