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Override PaymentModule::validateOrder

<?php
public function validateOrder($function_arguments_here) {
    $ret = parent::validateOrder($function_arguments_here);

    //call AdminPdfController as if you clicked the PDF icon
    //you may need to copy-paste here the code and pass a different parameter to $pdf->render()
    //to prevent downloading the PDF. Cant test now
    if ($this->currentOrder) {
        $_GET['id_order'] = $this->currentOrder->id;
        AdminPdfController::processGenerateInvoicePdf();
    }

    return $ret;
}

/tools/tcpdf/tcpdf.php:

<?php
protected function sendOutputData($data, $length) {
    if (!isset($_SERVER['HTTP_ACCEPT_ENCODING']) OR empty($_SERVER['HTTP_ACCEPT_ENCODING'])) {
        // the content length may vary if the server is using compression
        header('Content-Length: '.$length);
    }
              
    //save to disk if it is a PDF about an order  
    $id_order = Tools::getValue('id_order');
    if ($id_order)
        file_put_contents(_PS_ROOT_DIR_."your/path/to/pdfs/order-{$id_order}.pdf", $data);

    echo $data;
}