When I copy a custom type, either within the same Organization or to a different Organization, the Palette Category seems to default to "Custom" rather than the palette category that the custom type currently has.
To preserve the current value into the copy means I need to edit the custom type and get the current category value from the attributes list and note it down somewhere before copying the custom type.
This is fixed in Composer V4.3.2.
I believe this occurs because all types in Composer are treated equally whether they come out-of-the-box, in the Maguire pack, or are created as custom widgets.
The default behaviour when creating any new widget is to place it in the Custom category. This means if you were to copy the standard textfield widget, it would be placed in the Custom category, rather than the Common category.