Lorenzo,
Yes, I received the credentials and just got a chance to look into the issue. First, everything in the admin area looks to be configured correctly. So, then I went and found a page with a Like button on it. To test, I was using the page below:
http://www.liveandshop.com/index.php?option=com_k2&view=item&id=118:test
When I click the Like button, our Javascript is executing properly to notify JFBConnect that a new Like is triggered. This calls a page from your site in the background which then, should execute the AUP integration. However, instead, there's a Javascript error appearing that the URL we're calling can't be reached. If I go to the page directly, I get a 403 forbidden message. You can try yourself on the following URL:
http://www.liveandshop.com/index.php?option=com_jfbconnect&controller=social&task=likeCreate&href=http%253A%2F%2Fwww.liveandshop.com%2Findex.php%253Foption%253Dcom_k2%2526view%253Ditem%2526id%253D118%253Atest
It's a long URL, but that's normal. I'm not sure why that page won't load. Since it can't though, that's why the JFBConnect -> AUP code won't execute. There are a lot of things that can prevent some URLs from loading (being forbidden), anything from an agressive firewall to a problem with your .htaccess files rules.
Either way, if you can investigate what's preventing that page from loading, that should resolve the problem. Hope that helps and isn't too confusing. Unfortunately, I don't really know what's causing the forbidden error so I can't help narrow it down much further.
Best of luck,
Alex