IIRC, I had a telephone conversation with the no. on here
www.gov.uk/employment-support-allowance/how-to-claim
I had to send in DD's birth certificate and medical certificate to a JobCentre Office. They put her in a support group and paid a weekly amount.
Eventually, they send you the assessment form as part of the infamous Atos capability for work assessment. You fill it in, and submit any extra evidence you want. They may call your son in for an assessment at one of their centres. Be careful, they play a number of tricks on claimants - like the centres do not have car parks sometimes, forcing claimants to go on public transport or walk some way from the car. The centres may be upstairs. Then they can claim there are no problems with mobility, or getting to work on public transport. They may leave the claimant waiting half an hour - so they can say, the person can sit and work quietly. They may ask by way of conversation, if he watches East Enders - so again, they can say he has no attention problems.
In DD's case, I refused to go to the centre with her - as she can't go on public transport; walking any distance from a car is risky with her; and stairs pose a risk to her. I told them I wanted an assessment for her at our house. Anyway, they decided just on the papers, that she did not need to go through an actual assessment and awarded her the ESA with a severe disability premium.
She was already getting DLA at the highest rate for care and mobility; and it had no effect on that. She was not called in to re-apply for PIP.
Two and a half years ago, when DD was in the 6th form, the fact she was in receipt of DLA and I was in the process of applying for ESA, meant she was eligible for the school to apply for a bursary for her, worth £1,200 pa. The school gave us the choice of specifying what it was spent on for her; or we could give it to the school and let them choose. We let them choose - they bought her some software for dyslexia, a camera and an Ipad (which they used in class for work, because most of the students had one)
It is a process you need to keep on top of, far more so than applying for DLA - IME, it was riddled with delays.