Thanks for the images, I hadn't seen those yet.
The Sariucak link has great info about this overprint. Its very hard to find good information on stamps of Turkey. I don't remember if I read this on that site, but on a genuine overprint if you draw a line from the bottom horizontal line of the P, it goes under the bottom horizontal line in the R then lines up with middle line of E. Also read that middle line of "E" is almost as long as top and bottom, but at least one example in the above images seems to show a short line there.
Here's one I found with a PF cert. Later impression with broken upper frame?

And another I found that looks similar. Frame not as thick, and first "I" not as close to frame, leg on "R" is off, but pretty good forgery.

I have looked at a bunch of these, with only 1 or 2
possibly being genuine. I would love to see any more examples with certs or trusted expertizer marks.