I think there is an issue with this one (spoiler below).
After L1 M2 J1 M1, black is able to live with L2, but the move is rejected.
However, after J1, whilte should play L2 which seems to be the critical sequence. Then black has no choice but to follow the moves in the suggested answer.
I do not understand the solution to this one.
At the end of the suggested answer (supposed winning for black), Black is lost. If Black plays C4, then A2, and white can recapture to remove all the eyes.
I didn’t look for very long but I can’t find a solution to this problem.