I highly doubt Israel, even under Begin, supplied weapons to Argentina during the Falklands War. It is more likely that Israel supplied weapons beforehand. If it is true that Begin did supply the junta with arms, I'm sure that it was for a better reason than mere vengeance. Like him or hate him, Begin probably had some (arguable) notion of Israeli national interest at heart (that's why this story seems so unlikely because I don't see how supplying the junta against the British benefits Israeli security). The book's author needs to delve deeper before publishing this kind of stuff.
Iraqi police fire tear gas as thousands of protests burst into Green Zone, storm Parliament (AP)
from the article: 'Begin aided Argentina during Falklands War to avenge the British'