Spec-ing out developed projects

everyone,

I was tasked to create a Functional Specifications Document for a project awaiting approval for User Acceptance Test.

Just a background on our team's situation, we were assigned into the project on a much later time, so the one who's talking to the stakeholders is our developer. After gathering the requirements, our developer began creating the system and eventually he managed to deliver the application. The only problem is that our developer kept NO DOCUMENTATIONS of what the requirements are.

By this time, we got inserted into the project, but our only task was to create a user manual for the project and test it. During the development of the manual and the tests however, we were clueless as to what goals and what functions the application is supposed to complete. It goes without saying that we were unable to fully test the system, as well. So we came up with the idea of creating an FSD for the system so we can test it and then develop a manual for it.

My problem is, how do you create an FSD when the project's already developed? (Because what happens is that without the spec, you tend to see only how the system reacts to the test instead of deliver what it really is supposed to do)

I'm not really sure what I am supposed to look for, so I asked the question. My only reference to writing FSDs is Joel Spolsky's http://ift.tt/10vqkz0. But this one only tells about writing the FSD while the project is still being developed. In our case, the project is already done. Now we're just trying to test it.

Hope you can help me on this. Thanks.