They shot the no-frills film without anyone on the islands knowing what they were doing.
The film, whose title is a none too subtle a pun on the name of the islands and the protagonist's main purpose there - was made by a team of six, including the two actors, in just one week last December.
It will be screened in Buenos Aires later this month and the director says he intends showing it at the London Film Festival in November.
Convinced that to recover the islands it is better to make love and not war, Argentinian actor Fabian Stratas sets about trying to seduce one of the islands' inhabitants, played by British actress Camilla Heaney.
This tale of seduction may not be anything new.
But the fact that it was filmed without anyone on the islands knowing, using only three digital cameras and with no script to follow means that this is no ordinary film.
No-one knew
The film's team arrived in Port Stanley, on a commercial flight from Chile, and pretended to be private tourists.
They shot the no-frills film without anyone on the islands knowing what they were doing.
The British governor's spokesman on the island, Russ Jarvis, told the Spanish news agency Efe he did not know anything about it and could not comment.
It is the first Argentinian film ever made on the Falkland Islands - or the Malvinas Islands as they are known in Argentina.
It is also the first Argentinian film to be given the Dogma 95 certificate by the Danish film-making group that eschews special effects and excessive editing.
Other Dogme films include Lars Von Triers' The Idiots and Thomas Vinterberg's The Celebration - films shot naturally, without any artificial lighting, special effects or props.
Non-fiction/fiction cinema
In an interview for the Argentinian daily Clarin, the director, Jose Luis Marques, said he saw the film as "non-fiction/fiction cinema".
But he said that the film is not about retelling events on the island through his eyes, nor is it a film about the Falklands War, fought between Argentina and the United Kingdom in 1982.
He didn't want to make "a film that deals exclusively with the issue of sovereignty from the usual point of view".
He said he wanted to depict the relationship between an innocent islander and a young Argentinian aiming to produce a generation of Argentinian Malvinenses who in the future would be able shift the demographic balance on the islands.
Not all of the filming was plain sailing, however. At one point, leading lady Camilla Heaney began to feel a traitor to her country which created some tension among the team, Clarin said.
The film is using its own website to generate interest in the film, copying the same successful marketing strategy used by films such as the Blair Witch Project.
The site includes video clips, a shooting diary and hints on how to travel to the Falkland Islands.