Hello Alejandro (and everyone), Here is a possible solution for odoo v13 community edition:

1. Extend the PosModel (javascript) defined in point_of_sale/static/src/js/models.js, and override the push_and_invoice_order to save the order_server_id into the order object:

    models.PosModel = models.PosModel.extend({
        push_and_invoice_order: function (order) {
            // other operations
            transfer.then(function(order_server_id){
                // next line is important!
                order.server_id = order_server_id;
                // generate the pdf and download it
                if (order_server_id.length && !order.is_to_email()) {
                  //next operations
        }
    });

2. Patch the ReceiptScreenWidget, defined in point_of_sale/static/src/js/screens.js and override print function to make an server request of the pos invoice report with order server ids, saved when validating the order:

    screens.ReceiptScreenWidget.include({
        print: function() {
            var order = this.pos.get_order();
            // check the server_id lenth, server_id is an array
            if (order.server_id.length) {
                // print the invoice report with server ids saved
                this.chrome.do_action('point_of_sale.pos_invoice_report',{additional_context:{ active_ids:order.server_id, }});
            }
        },
    });

3. Extend the ReceipScreenWidet template defined in point_of_sale/static/src/xml/pos.xml to change button's label:

    
    
            t-inherit='point_of_sale.ReceiptScreenWidget'
            t-inherit-mode='extension'>
        
            
                 Print Invoice
            
        
    

Hope it helps someone.

Regards.