As noted in the story, the woman picking up money with the white hair was picking up the money so it didn't blow away. She gave it to Barberian when he walked back - his words.
The thing I find is stupid is that he is carrying a open cash drawer outside, even if it's over to the next door. That would be like me carrying the bank deposit money to the bank in my hands one block over from were I use to work. Even inside of stores you will see the cash drawers locked as they take them back and forth to the cash office for counting and re-floating.
I have to say either you have some real balls to carry open cash out side like that or you're a total idiot. I know if I had ever done that I would have been fired on the spot. When I did cash runs and bank deposits, the money was always locked and secured on me where no one could physical or openly see it. I think that would be commonsense when carrying large sums of money while walking to your destination.
Edit: You can see the contents (money) of each section in the cash drawer as he turns to go in the doorway, just as the guy starts to grab him.