You need to use Ajax to do this. Forgive me but my javascript is terrible since I haven't coded in it in a while but you need to set up an ajax request to that when the value of the select box is change it will send a request to the server to display that persons invoices. You can use

selectedIndex and onchange to get the trigger to work.

selectedIndex gets the current value that is selected and onchange is an event when the value is changed. Of course you will need to either addEventListener() or attachEvent() depending on the browser and use a ajax function to be the trigger that is called when the selectedIndex value changes. Since my JS is bad I really cant go any further than this hope this helps you some what.

If ajax is out of the question have a standard form that uses the value of the select box as the value being used in the query.