Rosalind Franklin did not share in the Nobel Prize. She died of ovarian cancer at the age of just thirty-seven in 1958, four years before the award was granted. Nobel Prizes are not awarded posthumously. The cancer almost certainly arose as a result of chronic overexposure to X-rays through her work and needn't have happened. In her much-praised 2002 biography of Franklin, Brenda Maddox noted that Franklin rarely wore a lead apron and often stepped carelessly in front of a beam. Oswald Avery never won a Nobel Prize either and was also largely overlooked by posterity, though he did at least have the satisfaction of living just long enough to see his findings vindicated. He died in 1955.
Watson and Crick's discovery wasn't actually confirmed until the 1980s. As Crick said in one of his books: "It took over twenty-five years for our model of DNA to go from being only rather plausible, to being very plausible ... and from there to being virtually certainly correct."