Will they backdate my PIP after tribunal win?

Hi everyone and I hanks for having me.  I've got a question and some great news... I won my tribunal on 4th February and was awarded the standard rate of PIP from 14th of January 2019 up to 13th January 2022, my question is whether anyone can tell me whether they'll backdate it for me??  I'm hoping so, I've been struggling so unbelievably hard for a couple of years to be honest and feel I genuinely deserve a bit of good luck.  I did contact the PIP and the lady confirmed it then took some details about my bank account and asked whether I'd been in hospital overnight at any point etc and told me that I should call back after 14 days if I've not heard anything.  I'm honestly not bothered about how long it takes to get a payment as I'm no worse off however I just want my monthly payments to start so I can start making a more comfortable life for my beautiful daughter and I.  Does anyone have any advice for me?  Thanks for taking the time to read this ??