I don't know - whenever I've tried to mess around with those flex winder things I have not succeeded much to my shame. BUT....
But before you dive in try this - just cut six inches off the plug end and throw it away with the plug and fit a new plug to the end of the cable.
Most of the faults I've seen on vacuum cleaners over many years have been caused by over enthusiastic tugging by the operator - over time the conductors in the cable stretch until they break in two and the machine suddenly stops working.
This suggestion may be a load of old rubbish but it's low cost, quick and easy and may save you lots of frustration.
Good luck...
Peccavi, April 2013