To make the speech even more consistent, you have to consider it as being part, for instance, of a story, a novel, or an article, in which the author talks about a person who was telling someone what had happened about the exam.
The passage could begin like this: "(name of the person telling) met (another name), and told him about the exam results."
Then it begins what is called a "free reported speech", which is a particular style used by many authors: the reported speech (reported by the person talking about the exam) that follows is not sintactically dependent by a reporting verb, meaning that the author doesn't write: "he said that", or "he told him that".
After having written "he told him about the exam results.", there is a full stop and the author goes on by writing: In his translation, John, where Peter had had "had", had had "had had"; "had had" had had the examiners' approval.
With this narrative tecnique, it wasn't necessary for the author to write "and that" after the semicolon, so that we can have all the "had" in a row, without other words in the middle.
If you try and read the speech imagining a context like that, you'll see that it "flows" better.