In my P-world musings, I am at some pains to avoid pinning down the P-world.  Indeed, the P-world is not an object, or thing of some sort, and considered as such, a P-world does not exist.  Husserl seems to have trodden a similar path in his later work, the Crisis of European Science.  In that work, he makes liberal use of the notion of the Lebenswelt, which, as far as I can see, is roughly co-extensive with the P-world.  Like any good phenomenologist, he clings rigorously to the centrality of lived experience, but with the Lebenswelt, he seems to move further from the silly idea that there might exist a technique that would allow you to capture, and then describe, experience in some raw form.  He also correctly points out the tragic consequences of ignoring the P-world/Lebenswelt by science.