Impossible puzzle?
Of course, that is checkmate. To be more clear, please explain to me why black should move c5 instead of c6++?

Of course, that is checkmate. To be more clear, please explain to me why black should move c5 instead of c6++?
Because it's a help mate puzzle. Both sides have to work together to mate black as fast as possible. If black mates white on the first move it's instant failure :p

Clearly... it is an illegal position... but let me have a look...

Because I saw no immediate threats, black could have held a very good position. I took 10 seconds looking at this, realizing black needed to walk into a blunder. Thankfully, blacks first move did. I only know this, because I checked the given annotation.
This isn't a real puzzle, it's a guess how you can get mated cherade.