Last Daughters of Krypton and Brainy Boys

Well established is the romance between Supergirl and Brainiac Five, the surrogate descendant of her and Superman's adversary, the android Brainiac. On occasion, she and the original actually battled, such as on the occasion when her cousin Superman finally enlarged the last surviving city, Kandor. While doing this, Supergirl used Brainiac's shrinking ray against him, seemingly eliminating him. 

Power Girl, like her doppleganger, had dealings with the fifth Brainiac's own cosmic twin, which didn't go so well. And later on, she would also have an encounter with Ultra-Humanite... his world's version of Brainiac...when she joined Infinity, Inc.

However, a persistent mystery involved what Power Girl's connection with another "brain baddie" was... namely Brain Wave. This villain, born Henry King, had been a psychologist with the mutant mental ability to project realistic images. From this, he built devices that pulled his victims into virtual dreamworlds, as he had with the Justice Society both when he first battled them, and then later with his "Dreams of Madness" as Dr. Forest Malone. 

This occured during the early to mid 1940s, during the time period when Power Girl as Kara Zor-L was travelling through interstellar space from her doomed homeworld to the same destination her cousin Kal-L had already reached of Earth-Two. And during the same time period that a young Henry King discovered his dreaming abilities, a scientist on Krypton-Two named Zor-L had himself invented dreaming technology for his daughter's Symbioship.

It would seem that during the decades of floating through the void, in a virtual Kandor modeled after the city she and her parents had resided in before the planet's destruction, her mind at some point connected with that of Henry. While he was unaware of this, she was aware of his existence, so much so that decades later when appearing for the first time as Power Girl on her adopted world, she was already aware of Brain Wave's plans.

Perhaps Henry was a virtual resident of Kara's Dreamworld Kandor, without even being aware of it. This city was so real, that an Earth-One Kal-El... Superman... could relate to Power Girl the experience of living amongst fellow Kandorians, knowing she had done so as well.