Source: https://www.prestashop.com/forums/topic/300119-solved-how-to-add-the-invoice-number-to-the-orders-grid/?do=findComment&comment=1517949
Try to start with adding another array item to $this->fields_list
add code to:
/controllers/admin/AdminOrdersController.php
‘invoice_number’ => array(
‘title’ => $this->l(‘Rechnung-Nr: ‘),
‘width’ => 50
),