BD
It usually takes the DWP 5-8 weeks to process a Tribunal Decision.
I know that you are nervous of contacting the DWP but it would really be worth your while calling them to make sure that they have the Decision Notice, it is frightening how many of these they lose.
It would be very unusual for the DWP to pursue the matter further but they do (as do you), have a further right of appeal, but not because they disagree with the Decision, only because they believe that there was an Error in the making of the Decision.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems