If the user story is totally a requirement from the user, should the BA ask the question so that the user says, "As a user, I want to... so that I can..."
I have heard people say that user stories should be requirements from end users. Don't take this too literally. TheThey do not literally expect:
Business Analyst: What do you want us to build?
End User: I need an easy way to do XXX.
Business Analyst: I'm sorry, that's not a valid user story.
End User: Ok. As a user, I want to XXX so that YYY.
Users aren't robots. At best, you'll get requests like "Can you add a button that does ABC?" Then you need to ask the user why they need a button that does ABC about 19 times to finally understand their problem and their end goal. Once you have this end goal, anyone comfortable writing it in this format can do so, with a few caveats:
Some organizations assign this responsibility explicitly to a Business Analyst, Product Owner, or occasionally a Lead Developer. This is at the discretion of the organization rather than some industry best practice.
The person writing the user story should be familiar with the "As a user... I want to... so that..." format.
When in doubt, ask your team or your supervisor. Don't over-think this.