Bug fixed
CellGrouping -> Manual isn't needed anymore for copying cell groups. They are copied correctly by default.
I'm trying to use:
NotebookWrite[nb, NotebookRead[EvaluationNotebook[]];
to copy cells from the EvaluationNotebook[] to a new notebook nb. For this, I move around in the EvaluationNotebook[] using different applications of SelectionMove[nb, ...].
Now, I would like to copy the exact same cell groupings of the current document as well, and this doesn't seem to happen. In the newly created notebook nb, I just see consecutive cells, without any grouping. Why is that? How can copying of groups be achieved?

CellGroupingRulesis preserved. But even withCreateDocument[NotebookRead /@ Cells[#], AbsoluteOptions[#]] &@ EvaluationNotebook[]they are not grouped properly. What is what makes them grouped then? – Kuba Sep 11 '13 at 07:22CreateDocument[NotebookRead /@ Cells[#], AbsoluteOptions[#]] &@ EvaluationNotebook[]with version 10.4.1 and found that all cell groups (including manually created) are preserved with the defaultCellGrouping -> Automatic. Looks like it was a bug which is currently fixed. – Alexey Popkov Jun 17 '16 at 04:27