The solution is really easy once you know that (i) the L-group is unconditionally dead, and (ii) turns the position precisely into a L-group where the outside White stones become totally useless. Spotting the move, is however another matter altogether. (For why the L-group is dead, please refer to the L-group page itself.)
What is noteworthy of here is that it prevents White from using the weakness originally present at by playing at either a or b (the latter sets up a throw-in ko at ). Due to this weakness, all other moves other than fail to kill White unconditionally.