Go for A, so you can find out what the reaper has in mind. You also get the bonus of a supporting character (the woman) who might react to being saved in a way that makes your character's life interesting, and perhaps not for the better.
I can see why you might want some feedback on this particular issue but, as well as it ultimately being your decision, there's not enough for us to go on. Saving the woman would be dramatic. Failing to save her would also be dramatic. But what's really important is what happens next. How does the woman's fate affect the story? Unless you can explain the significance of these two possible outcomes, nobody will be able to say anything either way.
Like `saintartaud said, both hold the power to make your story very different from one another. It depends how YOU want your story to go. Ask yourself, what would make a better story out of those options and if YOU were the reader, what would YOU PERSONALLY enjoy reading. Just work out both scenarios in your head/on paper and see which you think is more appropriate to your story and what you want.
Play out each scenario in your head, see which one is more interesting to you. Each option holds the potential for a very different story, so ultimately it's just a matter of what story you want to tell.