On inrau what did he find?
I figured this out just now.
It's not important what he finds.
It's important how what he finds will allow achamian to be manipulated and primed and positioned. What inrau finds is not important. What is important is that inraus death will make achamian into conditioned ground.
The key is, "Assist Drusas Achamian" letter that Proyas later receives from Maithanet. Maithanet or those pulling the Maithanet strings, want Drusas Achamian right where he is.
So what did Inrau find? Only what Maithanet wanted him to find.
Maithanet knew where Drusas Achamian was staying and his people knew that Inrau was contacting him. Maithanet is personally aware of Achamian because he asks Proyas directly about him. Presumably, the Thousand Temples knew that Inrau was former Mandate and untrustworthy.
So. Why then is an untrusted functionary allowed anywhere near the Shriah's private quarters? Because they let it happen. and Maithanet left a big old clue that only someone from the Mandate would recognize as a clue.
Why let it happen? Because Inrau is the lever that moves and conditions Achamian. They know this on Atyersus, and Maithanet, being who he is, would know or figure that out as well.
So what's going on here? I think the mandate needs to be prompted and prodded into place by Moenghus, and Moenghus needs to provide Kellhus a reliable Mandate tutor who won't report Kellhus. Otherwise, once Kellhus states his name, the mandate will swarm. and any spy will report him immediately. Unless that spy has recent reasons to distrust the Mandate. Problem: The mandate sorcerers don't distrust their school and have pretty perfect loyalty thanks to Seswatha.
So.
First, you identify a sorcerer with a weak spot; Achamian would stand out, he's a teacher who allowed a candidate to abandon the Mandate path before initiation. Then you leverage the situation so you can take advantage of the weak spot (if Inrau had went to be a steward in Cepharunni's household you would have arranged to send Akka that direction to be manipulated there).
Second, hunt down the Mandate spies and eliminate them one by one. You do this right before the Holy War will be called. For this reason of dead spies, the Mandate recalls the not-hunted-down Drusas Achamian to send him to be their new operative in Sumna (you know the Mandate will send Akka (even though the Mandate knows it alienates him modestly to exploit Inrau) because they're desperate to get quick access into the Thousand Temples).
Third, obviously, once the holy war is announced, Achamian is going to be sent to Momemn as he's the only active agent the Mandate has at this point, and they're already paranoid and turtled. But how do you manipulate that perfect Mandate loyalty Akka possesses because of Seswatha? That's the big question.
The answer is that you leverage the alienation he feels at the Mandate for exploiting Inrau by having Inrau murdered. This makes Achamian actively distrust the Mandate--especially in regards to how they treat his students.
You have Inrau murdered (reported as suicide) by allowing him to spy and leaving evidence only he could recognize, you let him commit the crime first so you can later allow enough info to leak through Proyas so that Achamian knows Inrau died working at the Mandate's behest. (note, Sarcellus may have been conditioned into murdering Inrau or Maithanet may have had another murder planned for Inrau that was 'foiled' by the Consult consultation Inrau witnessed, hard to say).
Boom. Achamian is betrayed by the Mandate and primed to be ultra-protective of his students right before Kellhus arrives. you've conditioned your way around the loyalty block of the Mandate and created a person who can teach your Anasurimbor without reporting the presence of a harbinger directly, instantly, back to the Mandate.
Additionally, but fairly irrelevant, note that the letter to Proyas arrives at almost the moment when Achmian is wrestling with whether or not to teach Kellhus sorcery. Inconveniently, Achamian was kidnapped by the Scarlet Spires because that letter, providing evidence they believed Inrau a spy, would have tilted Achamian further against the Mandate at that moment.