The woman in question is Brenda Maddox. See:
http://www.pbs.org/wgbh/nova/photo51/
I don't know how much credit she actually deserves; these matters of scientific discovery are often very complicated. But one side of the story at least is presented there.
"Without her knowledge, another Randall research associate, Maurice Wilkins, showed some of her X-ray diffraction photographs of DNA to James D. Watson, whereupon Watson, with Francis Crick, succeeded in determining the molecule's structure, and published in Nature magazine on April 25, 1953 an article describing the double-helical structure of DNA. Articles by Wilkins and Franklin illuminating their X-ray diffraction data supporting the findings of Watson and Crick were published in the same issue.
Franklin died of ovarian cancer in 1958 in London; it was almost certainly caused by exposure to radiation in the course of her research. Wilkins, Watson, and Crick were awarded the Nobel Prize in Physiology or Medicine in 1962.
Much has been written on the role that Franklin played in the discovery of the structure of DNA. While it is clear that her work was an important basis for determining DNA's structure, the correct deduction itself was mostly the work of Watson and Crick. Whether, given time, Franklin would have reached the same deduction in the rather competitive race (including such figures as Linus Pauling) to discover the structure of DNA is unknown. Watson has stated that Franklin should have discovered the structure of DNA as much as two years before he and Crick did.
Perhaps Franklin wouldn't have made the final discovery, but she did all the x-ray work that they used, and died of ovarian cancer from it in 1958. Watson, Crick, and the less-than-ethical Wilkins received the Nobel Prize in 1962. And none of them were ever gracious about her contributions. And they wouldn't have gotten there without her work.