Odoo Standard Coding style,  in most cases there exists a sub-method which is used to build the list of values, that can be easily inherited in your Module & append your custom values.

However while Invoicing, there exists couple of option such as 'Downpayment' etc in that case, the control will redirected to those related objects

Thus in your case, assuming you are following default flow of invoicing,  you would need to ideally write in the following manner.

@api.multi
def _prepare_invoice(self):
   invoice_vals = super(SaleOrder,self)._prepare_invoice()
   invoice_vals and invoice_vals.update({'x_inv_note': self.x_so_note,})
   return invoice_vals

Use this code to write into any field from sale order to invoice lines.

here i'm passing a field named order_type to invoice lines.

@api.model
    def _prepare_invoice(self, order, lines):
        res = super(saleWorkflow, self)._prepare_invoice(order, lines)
        if lines:
            for i in lines:
                self.env['account.invoice.line'].search([('id', '=', i)]).write(
                    {'order_type': order.order_type.id})
        return res