Bart gives an example of a classic use case and the break down of the business shows how you can start digging into what it really means.
One of key tenets of agile is to satisfy the customer, to do this you need to understand the customer. Classic Product Management requirements are often don't discuss the customer or user at all (The product MUST support concurrent downloads of data from multiple clients). In the example given her at least we have a user mentioned.
Instead of trying to parse the business case (or PRD requirement) its often better to step back and start with a more basic question "What is the end goal? When the user is done, what do they get?" At this point a judicious use of the "5 Whys" can help to make sure the end goal is really understood.
Once you know what the end is, you've got a start at an acceptance criteria. Now you need to figure out what needs to be done to get there.
A timeline exercise is excellent here, as it is really good at finding missing items. You start at a state of zero and start walking through what the user does to get to the state of done. For example, you're building a tropical resort and you want to offer scuba diving. It will of course help to understand the why and customer's done, but even if your stakeholder just says "because everyone else has it," the timeline can help. You start the timeline with the user in their hotel room and you walk through the entire experience until they are back in their hotel room.
Not only will this catch pretty much everything you need for the story, you'll probably pick up a lot of dependencies. For example, the docks where the scuba boats are is three miles from the hotel. You'll need a shuttle service, this is a whole other Epic and becomes a dependency to this story. Create an Epic story dependency, set that to the side and move on with your timeline.
So I guess in a round about way, my answer to converting business cases to user stories is "don't". Instead use them as a conversation starter to create user stories for the real user need.