The following story is from a person (female) who was in the field at the time and likely had connections with the people involved or knew people who knew them. Keep in mind that I could also be recalling it partly wrong but here it is:
Watson had the main idea about how DNA is structured and presented it to Crick. Together they managed to fix some issues and made a working model. There was only one question, how was it placed in the cell to which Watson had proposed it was the double helix. They basically had the whole thing ready but needed empirical evidence to make sure this is how it is and also to make their idea more credible once published. They heard about Franklins lab and the work they were doing along with a broad description of the photo. The people there would not be able to understand what they were looking at. So Watson (who may or may not have known Franklin prior to that, I don't remember) arranged a meeting with her to discuss her teams findings (he was a handsome fella, keep that in mind). He went to the lab and Franklin welcomed him. He immediately said "may I see the photo?" to which she replied "yes, it's right here" and handed it to him. Her understanding was that they would just talk about the photo so she offered some coffee. He agreed and when she returned with the coffee he was gone along with the photo. (Another person (male) from the field has told me that he got out of a first floor window but I think this is unlikely because he simply could have hid the picture and walked out the door as the woman who told me this story implied). The photo showed exactly what they were expecting and they would publish it with their paper. The problem now was that they had to justify how that picture came into their possession as it was obvious they couldn't have taken it themselves with no access to a suitable lab. They decided to credit the lab and after talking with some people from there came up with a cover story on how it was "given" to them.
