I've just recently used JW FLV Player (latest version) on a website and it works fine in FF and IE. I had a look at your source code and mine, and apart from obvious format/presentation differences, I noticed the line "sX.addParam('flashvars'" differs between yours and mine, you have a stray "&" at the beginning of the url. Also, I remember having difficulty in IE until I prefixed the url to the flv file with "../". You may want to try that.
Your code:
<div id="player">This text will be replaced</div>
<script type="text/javascript">
var so = new SWFObject('index_html_files/player.swf','mpl','480','295','9');
so.addParam('allowscriptaccess','always');
so.addParam('allowfullscreen','true');
so.addParam('flashvars','&file=http://85.131.50.136/aktur/index_html_files/janina3.flv&autostart=true');
so.write('player');
</script>
My code:
<p id='preview' style="margin-top: 0px;"><!--The player will show in this paragraph--></p>
<script type='text/javascript' src='video/swfobject.js'></script>
<script type='text/javascript'>
var s1 = new SWFObject('video/player.swf','player','640','360','9');
s1.addParam('allowfullscreen','true');
s1.addParam('allowscriptaccess','always');
s1.addParam('flashvars','file=../video/player_long.flv&image=images/vid_background.jpg&stretching=exactfit');
s1.write('preview');
</script>
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