ESA appeal success (I think)

I was placed in the wrag group towards the 52 week time limit for contribution based esa but I put an appeal in with the help of a welfare rights officer in my local area. I have received a letter from the appeal tribunal saying that the dwp have informed them that they have changed their decision in my favour and that my appeal case has now been closed. Can I assume I have won and been placed in the support group, and how long will it be before I receive any payments.