We had the chuck off this evening, it's a No.1 Morse taper. At the top of the visible spindle, just above the slot for the taper drift is an hex head grub screw. Dad forgot his imperial Allen keys, and I don't have any. We surmised as much as your drawing, that the extension screws on to the end of the spindle, but equally it may be on the Jacobs taper and the grub screw is there to retain it. Presumably, if it does come off then it's still possible to buy a chuck that fits it.