In Disgaea 4 - A Promise Unforgotten/Revisted Fuka believes everything is a dream or nightmare. When she first meets Desco she recognizes her to be the one who attacked her and believes the dream/nightmare is a result of being knocked out.
When the Hades Party goes to Earth Fuka found out that Des-X was the one who killed her, and since Des-X looks the exact same as Desco it explains why Fuka thought it was Desco.
But before invading the Information Bureau Desco admits she never met Fuka before, yet from the moment she was released she knew who she was (wanting to demonstrate her power to her Big Sis) and it seems Desco had been sealed up for quite some time given the other inmates and Axel knew about her (so she hadn't just arrived).
What I would like to know is the order of events between Fuka, Desco and Des-X such as which came first, Desco being locked away in Hades or Fuka being killed? And also how Desco knew who Fuka was despite never seeing her before?