At times like this you direct yourself to the Richfaces documentation, not the OTN forum.
Took me a 5 second google (richfaces a4j) and 2 clicks to find that. In total about 10 seconds of effort I'd say.
Thank you for your answer.
I knew about the a4j:jsFunction but I forgot to mention it.
My page is included in other page where the form resides, and I can not use this a4j:jsFunction because it somehow reloads the page and breaks it.
I have fixed this problem like:
<a4j:form id="requestWizardForm" ajaxSubmit="true">
<include page1> <---the page that holds the js script
var userTimeZone = userTimeZone();
var hiddenElementTimeZoneID = document.getElementById("requestWizardForm:clientSelectedTimeZoneID");
hiddenElementTimeZoneID.value = userTimeZone.timeZoneID;
var hiddenElementOffset = document.getElementById("requestWizardForm:clientSelectedOffset");
hiddenElementOffset.value = userTimeZone.offset;
Also, I want to thank you for your sarcams, helped a lot.