Additional information when VAT free

You can use an action hook for this, based on one of the examples in the action hook documentation (here).
This probably does what you need:

add_action( 'wpo_wcpdf_after_order_details', 'wpo_wcpdf_ex_eu_text', 10, 2 );
function wpo_wcpdf_ex_eu_text ($template_type, $order) {
    $is_ex_eu_vat = !in_array( $order->get_billing_country(), WC()->countries->get_european_union_countries( 'eu_vat' ) );
    $is_financial = $template_type !== 'packing-slip';
    if ( $is_ex_eu_vat && $is_financial ) {
        ?>
        <div class="ex-eu-text">this invoice is VAT free because it is shipped outside the EU.</div>
        <?php
    }
}

If you haven’t worked with code snippets (actions/filters) or functions.php before, read this guide: How to use filters

Thank you! This works great for me!
Is it possible to add a specific adress (Street X, City Y, Germany) inside of Germany to the list of countries that will get the message?
We offer a service where you can send your package to the german army headquarter which ist also VAT free.

Technically, that is certainly possible, but that’s a bit beyond the scope of free support. A web developer with some experience with WooCommerce should be able to do that for you without too much trouble though, especially with the above example as a reference.