Because the two regimes are waging propaganda wars against one another, so well known dissidents can't be killed because the opposing side would use that as evidence of the brutality of the regime they oppose. Such information may be used to destabilize regimes, cause civil unrest, and so they ship the well known dissidents off somewhere wherefrom whence they can'tcannot escape from, and where they can't cause any problems -- for a few years at which point they die from "natural" causes, accidents etc.
Keeping some dissidents alive for a while enables the regime to trot them out in the face of accusations as proof of their own benevolence.
The Falklands is nominally independent but really a satellite or puppet state with the US. This gives a veneer of truthfulness to their "exile". Alternatively they are exiled to some puppet state and escape from their to the Falklands as the security is much more lax in the puppet state. Add in a dose of bureaucratic inefficiency mentioned elsewhere.. slow paperwork, miscommunication to explain why security was lax maybe.