The functionality to move a Menu Item to another Menu Header is found in App Config/Menu Editor/Menu Editor tab.
1.Click on the Menu Editor tab;
2.Click on the Menu Item for which you wish to move to another Menu Header and the Editable and ReadOnly fields for the Menu Item will appear to the right;
3.The Menu Item placement under a Menu Header is determined by the ParentID. Enter in the ParentID that will result in the desired placement of the Menu Item.
4.Click "Save". Please note you will be able to see the changes but other users will need to log-out and then back in to view changes.