jQuery html() in Firefox (uses .innerHTML) ignores DOM changes_jquery

DOM:

function DisplayTextBoxValue(){
var element = document.getElementById('textbox');
// set the attribute on the DOM Element by hand - will update the innerHTML
element.setAttribute('value', element.value);
alert(document.getElementById("container").innerHTML);
return false;
}

jQuery plugin that makes .formhtml() automatically do this:

(function($) {
var oldHTML = $.fn.html;
$.fn.formhtml = function() {
if (arguments.length) return oldHTML.apply(this,arguments);
$("input,textarea,button", this).each(function() {
this.setAttribute('value',this.value);
});
$(":radio,:checkbox", this).each(function() {
// im not really even sure you need to do this for "checked"
// but what the heck, better safe than sorry
if (this.checked) this.setAttribute('checked', 'checked');
else this.removeAttribute('checked');
});
$("option", this).each(function() {
// also not sure, but, better safe...
if (this.selected) this.setAttribute('selected', 'selected');
else this.removeAttribute('selected');
});
return oldHTML.apply(this);
};
//optional to override real .html() if you want
// $.fn.html = $.fn.formhtml;
})(jQuery);