Likes on fanpage wall and on main website

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I also see you're using JFBConnect 3.1. The newest version, 3.2, was released a while ago and has updated all of the social widgets to use the most recent parameters available from Facebook. If you need to renew your subscription, please see:
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Thanks,
Alex

Ahh. I missed your previous subscription. Sorry about that.

The reason the Like counts differ is because the Like button on the page is referring to:
www.loswiaheros.pl/index.php?option=com_...&view=article&id=443

Whereas the Like button within Facebook is referring to the SEF version of your page:
www.loswiaheros.pl/australia/443-uluru-ayers-rock-olgas

In Facebook's eyes, these are 'different' pages, and therefore, treats the Likes for each separately. You can resolve this in a few ways:
* Update the Like button to specify the SEF version of the URL
* Add open graph tags to the page that would specify the proper canonical URL

The 3.2 release of JFBConnect adds a lot of support for Open Graph tags, so you could do something like:
{JFBCGraph url=http://www.loswiaheros.pl/australia/443-uluru-ayers-rock-olgas}
That should fix your issue. Additionally, the JFBContent plugin was greatly updated in the new release to handle the variety of URLs that Joomla can create better to always try and pick the 'best' one.

You can do these changes yourself without the new release, but it will be a much more manual operation.

Hope this helps, and good luck!