How to pass parameters to same form after form submission?
You can use the following code, to achieve what you want.

function submission_list_form_submit($form, &amp;$form_state) {
  $filter = array();

  if (isset($form_state['values']['filter_user'])) {
    $form_state['filter']['username'] = $form_state['values']['filter_user'];
  }

  $form_state['rebuild'] = TRUE;  
}


The form building function should then check if $form_state['filter'] is set.

function submission_list_form($form, &amp;$form_state) {
  if (isset($form_state['filter'])) {
    // …
  }

  // …

  return $form;
}


If the code doesn't work, use another array index instead of $form_state['filter']; it is probable that in such case the array index conflicts with the one used by Drupal or a third-party module. I would rather prefix the array index with the short module name, to be sure to avoid conflicts with other modules or future Drupal versions. 

References


drupal_build_form()