Ok, firstly, you need to understand that a private assessment carried no weight in a school. That is because there is no quality control. There may be excellent independent assessors around, but there are also those that diagnose whatever the parents pay them to diagnose
Secondly, dyslexia is a very broad term, with no specific definition, and most students who carry the label do not receive or require much in the way of additional support or consideration. Although, of course, it is useful to some extent that teachers are aware, but in reality, a quarter of a class may have the label, whereas a completely different subset of students may actually be showing the traits.
Laptops are not recommended, students with difficulties like this should be encouraged to write by hand. It strengthens and improves coordination, and developed neurological organisation in a way that laptops just don’t. It can seriously disadvantage a student to become reliant on laptops
Your son will be assessed according to his normal way of working. Neither an official, or private diagnosis of dyslexia, or anything else is relevant to this. School records are used, and evidence of how the student is normally supported is the basis for assessing what support is required in assessment.
So what has he had in the last few years? That is what he gets in assessment. Has he needed a TA to prompt him to continue to work, for example? If so, then that should be supplied during exams too.
Having said that, the time for collecting and collating evidence of normal way of working is long past.
I’m not really sure what you are expecting of the school, to be honest. I suggest you contact his head of year and explain what it is you want. Leaving aside the word ‘dyslexic’ , what specific recommendations for support were made in the assessment? Even if the school is unlikely to accept the assessment itself, they might be able to consider any specific recommendations separately