Hello,
Posting to index.php will give you no effect. Index.php is just a loader for the system, all the scripts and modules (including Login) are actually loaded via XHR (ajax) request and whatever POST or GET you set won't be passed to these calls.
But what you want can be quite easily reached with a simple work-around. Create new file in your EPESI folder named, for instance, login.php. In that file execute the following 3 lines:
<?php
define('CID', false);
include_once('include.php');
ModuleManager::load_modules();
...
With a script like that, you can pass data via post and get. Now, you need to implement a check that will identify the user - be very careful with that, you don't want any holes in this script - and once you identify which user it is, you can call method
Acl::set_user($epesi_user_id, true);
header('Location: index.php');
And the user will be logged in and directed to EPESI.
Again, your should be careful crafting that code. If you can post what kind of data string identifies the users (can you perhaps use EPESI password?), we can help you review the code to make sure it can't be abused.
Kind regards,
Arek