Yup, that's why I said they wouldn't do this, and neither would any other company that has a local division since they're already going to be subject to Argentine laws, and I assume based on OP's posts that their employer doesn't have a local Argentine division, but if they did, and they decided to let him do this while paying him abroad, they'd been in trouble legally on multiple fronts.
OP could issue invoices via the AFIP platform, it's the step that has to be done to get a control number for bringing the foreign funds in, and I don't think their employer would do anything with said invoices based on what they've said, especially since they're only of significance here ...