What links the constellation of the Reticle to this image, which science fiction fans will immediately recognize?
Yes, it's the famous and evergreen science fiction movie from 1979 A.D. called Alien: One of my favorites (right after the mythical Blade Runner), which I sometimes take a real pleasure in watching. It's a film that never tires me and every time I see it it's as if it were the first time: I always feel the same feelings of anguish, terror and fear despite knowing it almost by heart. When they enter the cave with all those eggs and the blue light... brr...
But let's go back to the initial question, the answer to which is ready. In the scenic fiction, the planet LV426, otherwise known as Acheron, and where the crew of the spaceship Boatswain meets/devests the alien being, is nothing more than one of the planets surrounding a star, which for the authors is ζ2 Ret. The reason for this choice will soon become clear: now let's see where this constellation is, in reality, in the southern sky.
The Reticulum is one of the many constellations introduced by Nicholas de La Caille, it was made known in 1763, after his death, and was called Reticulum Rhomboidalis, "Rhomboidal Grid", in memory of the instrument used by astronomers to place stars on the celestial sphere by measuring their position. For R. H. Allen, the first to identify it would have been Isaak Habrecht, a watchmaker from Strasbourg, known for his astronomical clocks.
Of recent origin, he has no mythology to support it.