Online work is a legal gray area. Technically you are not allowed to work as a tourist - at all. But if the work is not being done for a local entity, does that prohibition cover it? Logically, it shouldn’t; you aren’t competing with locals for that job, after all. And in practice, enforcement is all but non-existent - in any jurisdiction.
Although Fiscal may be in Argentina now with a "tourist visa" (that may have expired) it is safe to assume that he will soon have permanent residency, so that won't be an issue
Taxes, as nikad notes, is another story. Technically, again, you are working here and should be paying taxes here. But you almost certainly won’t be paying taxes here, at least not until you have a DNI. So for all intents and purposes just assume that your tax situation will be exactly as if you were still in the US.
Yes, technically, he will be working here and will be paid in the USA, but (as I recently wrote in a reply to one of your posts), if he stays out of the USA for 335 days of the year, the first $108K (USD) of his income will be exempt from federal income tax), so his tax situation will be radically different rather than exactly the same.
Once you have a DNI, you’ll have to decide whether you want to go the route of paying taxes here and seeking to reduce your US taxes as a result, or just continue as before.
Based on what Fiscal wrote about the concerns of the HR dept of his company, I don't think that is up to him.
The unanswered question now (which must be answered to appease the HR dept of his company in order for him to keep his job) is whether or not he can "legally" work on line for a US company that is not registered to do business in Argentina and (I am assuming) does not have clients who are located in Argentina. I seroiusly doubt any foreign corporation who does not have clients in Argentina would want to register in Argentina for the sake of one employee who wants to work remotely form Argentina.
If all of his clients are outside of Argentina and his company does not want to be registered in Argentina just so Fiscal can work remotely, I am assuming that the only option for him is to register with AFIP and pay income taxes in Argentina It will be the
only way for him to keep his job and continue to work remotely...and only if AFIP says it's OK.
I suggest he contact an Argentine accountant for further information. I also suggest that until he knows for sure what will works and what won't that he stays as far away from AFIP as possible.