If your strong hive has a few frames of sealed--only sealed brood place the sealed brood in the honey super and replace the brood frames with frames from the honey super the brood frame will draw bees into the super, the emerging brood( bees ) will be right about where they belong cleaning and polishing the cells, and migrate down to attend to brood in the lower chambers ( brood chambers ). As for the split, check for eggs and larvae in all stages of developement, if none immediately provide brood to prevent laying workers--if that occurs they will never accecpt a true queen. in the interm order a queen of the variety you want to populate the hive italian, starline, whichever you prefer, and if queen cells become present either destroy them or use them in yet another colony you want to start, introduce the new queen in the perscribed manner.--this is what I would do others may disagree.
Barry
Barry