[KWH]

First of all this is the play as I understand it:
4th and 4 for K on the K-25.
K1 punts and while the ball is in flight R1 gives an invalid fair catch signal on the R25. Upon seeing the Invalid Fair catch signal the Back Judge throws his flag and blows his whistle.
1) Assuming the ball crossed the ENZ prior to the Invalid signal and prior to the IW (which is highly likely), the PSK window is open.
2) The kick ended when the IW was blown!
3) The spot where the kick ended is (most likely) in advance of where the signal was given. Note: Logically speaking the ball was most likely blown dead in advance of R1, since R1 was (most likely) looking forward at the ball when he signalled.
4) Therefore the penalty (if accepted by K) is enforced from the spot of the foul (the R25) since the spot of the foul is (most likely) behind the end of the kick.
If the spot the ball was blown dead by the IW is determined to be behind the spot where the signal is given, enforce the foul from the end of the kick.
If the penalty is declined by K the down will be replayed.
Under no circumstances is K awarded a first down on this play.

Remember if you have the opportunity to make a play PSK, then by all means, MAKE IT PSK!