I just fixed the image in the previous post, the original was wrong sorry 
The solution:
Spoiler! Try to solve first!
The winning move is first J1 using the kothreat, to reduce the remaining dames, and then play B9 to fight and win that ko finishing it with A9 AFTER all dames have been filled. You can verify that way, white gets 41 intersections instead of only 40. If white plays B9 directly, black must not take A9 (that is a losing move!) but instead just connect J7, reverting to the same score as normal dame-filling.
The intuition is that the endgame in that case will finish with “black pass [or makes useless move inside self territory] , white fills A9, black pass, white pass”, instead of finishing “white pass black pass” as would end for normal dame-filling. So white manages to play one more time after black was forced to pass, getting one more stone on the board without black getting compensation for it!
Reasoning in territory terms (this should always be possible, as area scoring and territory scoring are equivalent, if territory is counted correctly with the same criteria as the area-scoring rule 
), the trick is that we can imagine that white passes after black passes, without playing A9. So white managed to keep it open in the end, and thus scores A9 as an extra territory, giving it a win.
A more detailed explanation of this same principle is in this other thread: https://forums.online-go.com/t/is-an-endgame-ko-worth-more-in-chinese-rules-than-in-japanese-rules