Adding items to another Modules Admin form
For the sake of clarity, let's say that your custom module is named CUSTOMMODULE, and the one you want to alter is ALTERTHIS.

You can use hook_form_FORM_ID_alter() like this:

/**
 * Implements hook_form_FORM_ID_alter() for ALTERTHIS_admin_form().
 */
function CUSTOMMODULE_form_ALTERTHIS_admin_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  // Alter the $form here.
}