How long does it usually take to get an award letter after winning a PIP Tribunal?

I’m looking for a rough idea as to how long it usually takes for an award  letter from DWP after winning a tribunal appeal, I asked DWP for an MR after they only awarded standard daily care and 10 points for mobility. I got a letter to say that they would award enhanced daily living but kept me at 10 points for mobility so I appealed to the tribunal. It didn’t take long to get a tribunal hearing date so I sent an additional bit of evidence from my GP and DWP sent al letter to me and the court to say although the evidence is compelling they didn’t have time to do anything about it. At the hearing the judge was not happy with that response from DWP and told them they were wasting court time as they told him they will award enhanced on both. The other part was that the judge wasn’t happy with was DWP wanted to keep the original award dates which would have meant a review in 11 month, I think that has been extended to 7 years. DWP also wanted to only backdate the money they would owe until July but the judge questioned that as my claim goes back to November 2020, he then ordered it to be back dated to November. DWP are telling me I won’t get award letter for another 5-6 weeks, surely that can’t be right.
thanks in advance for your help