@gypsywater
IF he was diagnosed by the NHS, it should be on his GP records. Everyone thinks we only have one set of medical records, but we don't, we also have hospital records, and a few more specialised things like MRI scans. All can be accessed by request.
If he was diagnosed privately, the assessment and results may not be with the GP because the NHS does not accept most private diagnoses. However, it seems from your parents' reactions that it was an NHS dx or that the GP and school both had copies.
If he needs to access his medical records, for starters, we can all look at a brief summary of our own GP records online. It's the same login you use to order repeat prescriptions and make appointments.
www.nhs.uk/using-the-nhs/nhs-services/gps/gp-online-services/
www.nhs.uk/using-the-nhs/about-the-nhs/your-health-records/
www.nhs.uk/using-the-nhs/about-the-nhs/how-to-access-your-health-records/
I needed copies of a lot of medical evidence for my adult DD's PIP claim a couple of years ago, that's how I know.
Nowadays in England they are free.
There is a huge backlog for NHS adult autism assessments, many areas had around 18 months to 2 years pre-Covid. no idea on the current status.
The NAS has a directory of people who can diagnose autism in adults privately. www.autism.org.uk/directory DO read the disclaimer.
For the diagnosis to be accepted by the NHS, the person or team who diagnose must also diagnose for the NHS part-time as well as in their private practice.
I'd talk to him about it, particularly if he does something that's common autistic behaviour like monologuing at you for ages about an interest of his with no clue you checked out of listening 10 minutes previously. 
Be straightforward, no hints or insinuations.
Comment nicely on the behaviour he's just shown, followed by 'have you ever thought you may be autistic?'
Depending on his response and if you think it's an appropriate thing to suggest, you could do an AQ test with him, it will be telling as to which answer you'd choose from your perspective of him and which one he chooses for himself, i.e how he sees himself.
AQ tests do not diagnose autism, they can pick out a likelihood of autism depending on the score and can be used as an indicator that someone would be a good subject for a diagnostic assessment.
Very short one www.nice.org.uk/guidance/cg142/resources/autism-spectrum-quotient-aq10-test-pdf-186582493
Longer version aspergerstest.net/aq-test/
Scoring for longer version aspergerstest.net/interpreting-aq-test-results/