Apparently, marriage + ARC is the magic formula, even if the ARC is not marriage-based, whereas an APRC without marriage is in a slightly different category.
This means Mr. Duke should still have permission to work even before he obtains the OWP, because he’s still married and still has an ARC (with a P added). Still, obtaining the OWP will make things smoother.
(This is not legal advice, so note the word “apparently”.)