The value of a multi-select is the concatenated options, so you have to build the string. You can either hard-code the string, or you can loop through the options to build it dynamically.
You must use javaScript for this. Put this code in the onClick of the button (make sure to update the ids):
var listOpts = page.F_SelectMany1.getOptions();
var s = "";
for(var i in listOpts) {
if(i > 0)
s += "__#__";
s += get(listOpts, i).value;
}
BO.F_SelectMany1.setValue(s);
Thank you So so much :)