Demonstrates simulated keyup event in vanilla JS. Tested in Chrome.

fh_password_change_bookmarklet.js

javascript:(function() {
  var $ = document;

  /// construct

  var old_password = window.prompt('Old password', 'Old password');
  var new_password = window.prompt('New password', 'New password');

  element('old_password').value     = old_password;
  element('new_password').value     = new_password;
  element('new_password_chk').value = new_password;

  var event = $.createEvent('KeyboardEvent');
  event.initEvent('keyup', true, true, window, false, false, false, false, 9, 0);

  element('old_password').dispatchEvent(event);
  element('new_password').dispatchEvent(event);
  element('new_password_chk').dispatchEvent(event);

  element('submit').click();


  /// functions

  function element(id) {
    return $.getElementById(id);
  }
})();