While this is an old thread, this is probably relevant to anyone who comes across it. The number to send an SMS to a mobile in Argentina is the same as the number to call. However, the number displayed on a received message is probably the number to use within Argentina, so a reply to a received message may not work.
The main reason for this post is to say that apparently SMS sent from some, but not all, senders reach a recipient in Argentina. I found that sending SMS from a Vodafone UK mobile to Argentina didn’t work; sending it to exactly the same number from a web service (call 18866.co.uk; no longer available) the message did reach the recipient . So all I can say is try different services and see which work; and don’t rely on a message being delivered. HTH
Added: just tried 9 June 2011, confirm that SMS sent to an Argentine mobile from Vodafone UK fails silently; SMS sent from a computer using VoIPcheap.com software works (sent by holder of paid account). Message sent FROM Argentina comes with wrong number for international dial/SMS reply (9 must be inserted after “54” country code).