Kathleen, maybe try putting this discussion in the Prince autograph forum and see if you might get more responses. Just an idea.
But yes, I’m certain this is authentic.
The base of the P looks a bit jumbled, but consider the surface of what Prince was writing on. A napkin, or something like that, is not a smooth surface. It makes signing more difficult. Yet it still looks very good.
If your friend has anymore he wants to give away, I’d be a happy recipient!