Absolutely, yes.

He got a 3-month custodial sentence. Convictions resulting in custodial sentences shorter than 12 months become 'spent' 12 months after the sentence ends. So, his conviction will be 'unspent' for the next 15 months.

While his conviction is 'unspent' he still only needs to tell an organisation about it (e.g. for a job application) if they ask him, but it will show up on any DBS - basic, standard or enhanced.

After it becomes 'spent' it will only show up on a standard or enhanced DBS check. He only needs to tell a potential employer, university or college about it if they ask him to and they tell him the role needs a standard or enhanced DBS check and it has not been removed ('filtered') from DBS certificates (as it resulted in a custodial sentence, it can't ever be filtered).

It's against the law for an employer, university or college to refuse someone a role because they've got a spent conviction or caution, unless it makes them unsuitable for the role (i.e. a driving conviction might make them unsuitable for a job as a driving instructor).

Well since he was convicted of course he does.