I can see that you've been solving this with Radek in the ticket, so let post here some updated info:
Well, if your Smart search filter does not use post-back (Filter auto postback: disabled) it generates query parameters with selected filter values, e.g. &wf=2;&ws=0;&wa=0, where wf determines what option has been selected in filter. You could pass this value to page containing your smart search result web part. This page could contain also hidden smart search filter (Visible: false) which could process this query string and filter result displayed in Smart search result web part.
However, I would recommend to clone Smart search filter web part for this second hidden instance, as you may need to update its code-behind and ignore StopProcessing variable. This will be true if the web part is hidden, so it would not process the code. But, in this cloned instance you can ignore it or set it back to true.
Other option would be deveoping custom filter with complete custom functionality as per Developing custom filters
Best regards, Martin