Conspiracy's Masterstroke: Illusory Assassination

Momo Hinamori vs. Izuru Kira is small scuffle that takes place during the Ryoka Invasion but between the Shinigami themselves. Remembering the prior warning given by Tōshirō Hitsugaya the 10th Division Captain of Soul Society regarding Gin Ichimaru the 3rd Division Captain, Momo proceeds to attack Gin for the murder of her Captain Sōsuke Aizen.

Battle
As Momo Hinamori is running late for her lieutenant meeting, she is in a rush but as she is running she sees her Captain, Sosuke Aizen brutally murdered and pinned to the wall with his own Zanpakutō.

Hearing her scream Izuru Kira, the Lieutenant of the 3rd Division, Tetsuzaemon Iba lieutenant of the 7th division and Rangiku Matsumoto lieutenant of the 10th division reach the site and witness the horrific murder of Captain Sosuke. Ichimaru Gin also reaches the scene but an enraged Momo attacks him suspicious that he was the one who had murdered her Captain. However her Zanpakutō is met by Izuru Kira's who says that what ever the reason he would never let another raise their sword against his Captain. Momo pleads for him to step away but instead he tells her to sheathe her sword. Momo loses her patience and releases her Tobiume. Kira, seeing that she is serious, releases Wabisuke too but they are stopped by the timely arrival of 10th division captain Tōshirō Hitsugaya who places them under arrest. As the two are escorted away, Hitsugaya accuses Gin of attempting to kill Hinamori and warns him that if any harm befell Hinamori then he would kill Gin.

Aftermath
The fight ends with the arrest of both Momo Hinamori and Izuru Kira. Finding the body of a Gotei 13 captain murdered in such a gruesome way set the stage for the mindset the Gotei 13 would have against the invaders. The conflict also started the divide between those following orders and those following their conscience.