While I cannot claim to know all about Cyberboard, here is one method I have been using for managing the units:
Here I have selected the Cavalry Corps of Pahlen III.
|here the cursor is over the unit showing the data|
|now the corps text box is ready to edit|
|The section to be 'cut out' is highlighted the 'control x' will cut it and hold it ready to be pasted|
|left click and hold while dragging the new unit onto the mapboard|
|after entering the cut data, I go back and copy the formation - then with the header 'detachment' to identify that the unit is not the sole or parent formation|
Then completing the change by updating the parent Corps formation data.
|updating the parent Corps formation data|
|selecting the troops for stacking|
|once they are all 'stacked' together you will be able to shift around the entire stack|
I hope that you find this little tutorial on unit splitting helpful.