Congrats on winning the appeal!
The Tribunals decision has now been sent to the DWP (the government department who process the PIP claims) to action.
Assuming the DWP are not planning on appealing the decision further, there is no strict timescale in which they need to pay the claim, but normally within 4 weeks you will have received a letter from them, confirming the award of benefit, what your rate and regular payments will be, and the amount of backpay. If you haven't heard from them within 4 weeks, I would recommend calling them on 0345 850 3322 to chase (you can of course call them much sooner - no harm done!).
At the back of your mind, do bear in mind that the DWP have up to one month to consider requesting a 'Statement of Reasons' from the tribunal if they wish to consider appealing the decision further, and that this can sometimes delay matters. It is in fact rare for them to do so, but I just thought I'd make you aware. The first you would know about this would probably be the Statement of Reasons in the post from the Tribunals Service, and if you receive one of these I would recommend re-posting for further advice (the reason I won't go into it all now is that it's so unlikely).
Hope this helps.