Question: We need to do some user documentation for a product we have been working on for the past few sprints. We are now starting a new project in the next sprint and the PO is making the documentation for the product produced previously a User story for this sprint.

I am just wondering your opinion on this approach. Personally, I don't agree that documentation is a User Story within Scrum because it doesn't produce any code. 

EDIT: Thanks for your opinions guys. I had it in the back of my head that a sprint was to implement an increment of working software, but your views have changed my outlook. Thank you for all your answers.

Answer: 
"As a user of X, I need to know how X works" seems like a legitimate user story to me. This could result in written documentation or online help.

The point isn't just code--it's meeting the users' requirements.
In our organization, the tooling team, in charge of our maintaining and enhancing our continuous integration system is using Scrum to help them manage their work. They are not writing code but they are practicing Scrum nonetheless.

To answer your question specifically, I would ask if the team considers that the documentation is part of the "Definition of Done" or not. 

If the team considers that the documentation is part of the "definition of done" then, there is no need for an additional story and the story cannot be accepted unless the documentation is written and validated.

If the team considers that the documentation is not part of the "definition of done", I would create a separate story so that the Product Owner can manage their work.