The pope is not going to involve himself in this dispute. He dislikes Kirchner, and is unlikely to put that aside to aid her in election-related chest-beating.
I’m not surprised the pope believes the islands belong to Argentina. You’ll find 90% of the Argentine population believe the islands belong to them, just as 90% of Turks will say Northern Cyprus belongs to them. The pope is free to have his opinion on these kinds of things. It has nothing to do with the church at all, and is simply a geopolitical matter.
Now, in my opinion, the Malvinas are a fictional group of islands. Argentina’s claim to the territory is weak historically, from the evidence available, and was made even weaker by an invasion in the 1980s, in which they were defeated fair and square.
I believe Argentina also has some sort of border dispute with Paraguay, and I have no doubt the pope would come down on Argentina’s side there. Is he going to funnel Vatican money to Kirchner so she can invade Paraguay? Unlikely.
Not counting the Swizz Guard, how many divisions does the Pope have? Hardly likely that the Vatican would declare war against the Brits.
Argentina’s claim to the Falklands is stronger then the US claim to California. England should leave the Falklands, the north of Ireland, and Gibraltar; filling these places with your own settlers then using them to legitimize your claim is absurd; if any of these places were Muslim they would have already won their independence.