Out of Check Into Check

Back to chess. As I recall, we were discussing illegal moves. That is to say, my opponent would make an illegal move (leaving his king in check) and I would answer his illegal move with one of my own: capturing his king. One good illegal move deserves another. Tit for tat. I thought we were done with illegal moves but I came upon the rematch game, where my previous opponent again made an illegal move, this time moving his king out of check into check. I know you are just dying to see that game so here it is. Same opening, same color as in the previous game:
1.d4 Nf6 2.c4 e6 3.Nf3 c5 4.d5 ed5 5.cd5 d6 6.Nc3 g6 7.e4 Bg7 8.Qc2 O-O 9.Bg5 h6 10.Bh4 g5 11.Bg3 Nh5 12.Be2 Ng3 13.hg3 Re8 14.O-O Qe7 15.Nh2 Nd7 16.Ng4 Ne5 17.Ne3 g4 18.f4 gf3 e.p. 19.gf3 Bh3 20.Ng2 a6 21.Kf2 b5 22.Rh1 Bg2 23.Kg2 Rac8 24.Nd1 f5 25.Ne3 fe5 26.Nf5 ef3+ 27.Bf3 Qf6 28.Raf1 Nc4 29.Bg4 Qb2 30.Qb2 Nb2 31.Nh6+ Bh6 32.Bc8 Kg7 33.Be6 Re7 34.Rh4 Nc4 35.Rg4+ Kh7 36.Re4 Ne3+ 37.Re3 Be3 38.Re1 Bg5 39.Rh1+ Kg7 40.Kf3 c4 41.Kg4 Bh6 42.Kf5 Re8 43.Bd7 Re5+ (At this point he played the illegal 44.Kf4. Since we were not in blitz mode I did not capture his king with my bishop. Instead I called the TD over and he added two minutes to my clock.) 44.Kg4 Rd5 45.Bc6 Re5 46.Rd1 c3 47.Rd6 c2 48.Rc7+ Kf6 (0-1) White had 3 minutes remaining at the end; Black, 18 minutes.