FWIW
I think either report formally to STA ( my recommendation because I work in the system and have to advise that ) or don't report at all. Not the option you have/are about to take.
I think it is unfair for the HT to have this hanging over him, he can't undo his cheating now, even though he knows you know. You are also not in a position to investigate, what if you are wrong!
Yes, he may decide to report himself to STA ( but then he has already completed and returned his HT declaration at the end of the week, confirming everything is in order), he may decide to talk to his CoG ( or trustees), who may also decide they must report.
When I've carried out investigations, via the LA on behalf of STA, when it is a complaint by a parent, we know who the parent is (not that relevant to us because we don't know the parents in schools) but we do not share the parent’s name with the school.
We talk to staff present in all tests. Best case is that the staff member accused of cheating has had another adult with them at all times and this adult verifies that nothing untoward had taken place in any tests.
This might involve numerous other adults (more than one in the test room, or different second adults in other tests).
Good practice is also that no staff member or adult reads the test papers, to maintain the integrity of tests ( other than if they are a reader) again, if this is practised and all staff are saying the adults didn't even pick up the paper there is a confidence in tight systems and limited risk of an adult having the opportunity to cheat.
Dependent on the other adults’ responses we might talk to children but only in a very general sense.
The last investigation I carried out, it when we met with the HT at the school, it turned out that there was a parent making vexacious complaints, overtime, about many different things.
In that case, the HT had a very good sense of who had made the complaint to STA (although we didn't confirm who it was).
We found during the investigation that in the school all tests rooms had more than one adult. All adults we interviewed (9 used in different tests/test rooms across the week) confirmed that no staff members had picked up and read papers or helped any child. Adults confirmed that there had been two staff members present, when a third adult had to remove a sick child. All added up to very tight systems.
Report written to STA and STA decided no case to answer. The school was monitored again by the LA, unannounced, as requested by STA, the following year, with nothing untoward found.
A much more serious case, involving HT and Y6 teacher, took many days of interviews with staff, matching childrens work to test papers, talking with children, but that was as the result of a report by the Chair of Governors, when his own child disclosed cheating in the tests, to him.
All systems, under investigation were found to be lax, senior staff reported that they felt ‘excluded’ from test rooms. There was lack of other adults in test rooms, with only HT/Y6 teacher invigilating.
Evidence gathered from adults, children, children’s books and teacher planning showed that HT &Y6 teacher had cheated to raise standards as the curriculum had not been fully taught.
A very long process (2 years) with the HT and teacher both lost their jobs and were barred from teaching. This school, even with a different leader, also had unannounced monitoring visits ( before, during and after test week) the following year.