El archivo php de moodle encargado de cerrar la sesión es el siguiente: (prestad atención solamente a la penúltima línea del código, pues el resto está bien. En esa penúltima línea no sé cómo llamar al .jsp)
Código PHP:
<?php
// This file is part of Moodle - http://moodle.org/
//
// Moodle is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// Moodle is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Moodle. If not, see <http://www.gnu.org/licenses/>.
/**
* Logs the user out and sends them to the home page
*
* @package core
* @subpackage auth
* @copyright 1999 onwards Martin Dougiamas http://dougiamas.com
* @license http://www.gnu.org/copyleft/gpl.html GNU GPL v3 or later
*/
require_once('../config.php');
$PAGE->set_url('/login/logout.php');
$PAGE->set_context(get_context_instance(CONTEXT_SYSTEM));
$sesskey = optional_param('sesskey', '__notpresent__', PARAM_RAW); // we want not null default to prevent required sesskey warning
$login = optional_param('loginpage', 0, PARAM_BOOL);
// can be overridden by auth plugins
if ($login) {
$redirect = get_login_url();
} else {
$redirect = $CFG->wwwroot.'/';
}
if (!isloggedin()) {
// no confirmation, user has already logged out
require_logout();
redirect($redirect);
} else if (!confirm_sesskey($sesskey)) {
$PAGE->set_title($SITE->fullname);
$PAGE->set_heading($SITE->fullname);
echo $OUTPUT->header();
echo $OUTPUT->confirm(get_string('logoutconfirm'), new moodle_url($PAGE->url, array('sesskey'=>sesskey())), $CFG->wwwroot.'/');
echo $OUTPUT->footer();
die;
}
$authsequence = get_enabled_auth_plugins(); // auths, in sequence
foreach($authsequence as $authname) {
$authplugin = get_auth_plugin($authname);
$authplugin->logoutpage_hook();
}
require_logout();
//hago la llamada al jsp
include "http://MI_IP:MI_PUERTO/MIJSP.jsp";
redirect($redirect);
?> 
