Well, the solution's quite simple really - you're missing the $quote variable in the "Body" textarea. So what you have at the moment is :
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{$ubbt_lang['POST_TEXT']}<br>
<textarea cols="$TextCols" rows="$TextRows" class="formboxes" wrap="soft" name="Body"></textarea>
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it should be :
{$ubbt_lang['POST_TEXT']}<br>
<textarea cols="$TextCols" rows="$TextRows" class="formboxes" wrap="soft" name="Body">$quote</textarea>
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note the $quote []/forum/images/icons/smile.gif[/]
that is all.