It's fake. Someone just edited the two versions together and incorporated a bit of the instrumental found in that video of Kanye and Diddy in the studio. You can hear the choppiness around the end of Ye's verse.
I 100% believe that Kendrick's verse isn't even from a remix but is just a reference verse like a lot of people are speculating. I bet French and the other artists credited as 'composers'/'producers' did similar verses and Kanye meshed them (the flows, I mean) all together for the final version.