Payments when a child moves from dla to pip.

Hello all,
Recently I helped my sister in law complete the forms for my niece changing over from dla to pip as she turned 16 in Feb. We used the guides on this website to complete the forms.
We were successful in getting my niece awarded enhanced on both elements from 2nd Sep 2026 until 1st July 2032. She has been getting dla at higher rate care and lower mobility.
The letter that my sister in law recieved (she is appointee for my niece) state that she will recieve the first payment on 29th Sept for money owed up to 28th Sept. She is a bit confused about how payments will work.
The next dla payment is due on 1st Sept. So will she get that payment then the pip payment on 29th Sept and then every 4 weeks after that?
And as it says the pip award is from 2nd September, does this mean that the difference in the mobility elements wont be backdated to when the forms were received?

Thanks in advance for any insights.