Snelgroves recommendation was separation by an excluder then one or more honey supers, then the double screened division board. Cells have been started every time for me with that method. On recombining the two colonies I have often removed the old queen but sometimes have left them to their own decisions and have no queenless developments.
The Snelgrove method is more than simply placeing a double screen between halves of a split colony.
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