Will I get the PIP benefit until the tribunal?

My sister recently had a PIP (from DLA) assessment ,face to face. She has not received the decision yet, but has had the assessor's report of the interview. She previously got the higher rate for mobility but nothing for personal care. It seems that her PIP will be the standard rate for both mobility and daily living.
Although her mobility is very bad, and she explained, both on her form and in person to the assessor that she can only walk less than 20 metres , he didn't agree. The assessment was in rooms in a local hospital but she was unfamiliar with that part of the hospital so her son went the week before to check out the parking and the location of the assessment. It was obvious to him that his mum would not be able to walk that far, so on the day her husband pushed her in a hospital wheelchair as far as the waiting room. She was asked to follow the assessor down a corridor. She managed this , using her normal walking stick and leaning heavily on her husband. Now she has had the report and it states that the corridor is 23 metres long and she walked it with the aid of her walking stick. No mention of her husband or the fact that the assessor had his back to her until they reached his door. There were many other inaccuracies in the report but I won't inflict even more of them on you. As you may appreciate, once she gets the dreaded brown envelope with the decision she will ask for a mandatory reconsideration and then appeal to a tribunal.
My main question is - Will she receive the PIP awarded to her (standard mobility and care) while the appeal process goes through ? Or will the fact that she is appealing the decision just stop her benefit?
She has a motability car, which she is likely to lose before the appeal process is finished, and she really needs a car to get about. If she has neither DLA nor PIP she will find it very hard to pay for a car of any kind.
I would be very grateful if you could answer this question. I am awaiting my own "invitation" to migrate to PIP from DLA and would like to be as informed as possible. As you say, knowledge is power but sometimes I feel very powerless.
Thank you in advance, Barb

Thank you so much for your help. It is a real relief to know that. I wasn't expecting, but I was hoping, that would be the case.
Thank you,
Barb.