His setup was established to be during the mock trial. There wasn't any issue with the time frame, since once the trial started, his recording gave him a nice wide 20 minutes to work with.

He really should have kept a spare staff.

A certain issue comes in when Hugh testified to not seeing the professor. Hugh would have gone up to the stage after Means finished his "speech". Means' excuse of being in the bathroom would have been logical had he returned immediately after his work was done. What reason did he have for not showing up right after? He could have solidified his alibi just a bit more if he had other students notice him there up until the police arrived to stop the trial.

It wasn't the real murder weapon, but it had the victim's blood. I think Means put the victim's blood on it, since it was supposed to be used in the mock trial, so he knew Junie would take it.

Why did Hugh got on the crane before mock trial, again?

He was supposed to get to that job of his earlier, helping to clear the stage of stuff and all, but didn't, maybe even slacked off. Then, he had to get it done before the stage was to be used the next day for the festivities, and he only had that time then to finish the job, since he's going to star in the mock trial later.

Why did Hugh lie about seeing the body before the mock trial?

Awl belonged to Courte and was murder weapon. The staff had traces of blood, because he stuck it onto the victim's wound (staff was only a metaphor...) And it's not mentioned, because there is no longer reason to discuss it.

"Ends justify the means." He wanted the trial to end as quick as possible, since he suspected Juniper was the snitch who reported him.

No, that's not it. The awl was only used as a decoy. Means had one pointy thing with him when he confronted Courte. She would have no reason to have a painted awl with her, so he couldn't have held the awl in his hands at the time of the murder.

*spear was the metaphor, I meant. Sorry. But then, it turns out it wasn't. But I didn't see any edge on that...

You underestimate how sharp a man's "spear" can be.

Is there any unique dialogue when you claim Det. Arme is the phantom? If yes, what is that?

There isn't. I mistakenly thought "the detective leading the evacuation" was Arme the first time I played through this case and tried presenting her profile, but got a generic response telling me I was wrong.

And someone said that there was, in 5-3 when talking to Klavier. I finished 5-3 a few days ago and I thought I had squeezed every last bit of text out of him through talking/presenting but I didn't see any mention of Kristoph. Does anyone have what he said or can point me in the right direction to find out what he said?

When Phoenix mentions that he's seen the black Psyche-locks before

What if... Kristoph never knew about Shadi Smith being Gramarye. He killed him, not sure if he's the real Gramarye or not? (Just a theory.)

...Wait, what? I don't really can comprehend what that would be supposed to mean... xD

I think that's a very possible theory but what you mean about the last part?

I'd say it's impossible theory. He would have no reason to go through that hidden tunnel at all, if it wasn't for seeing that familiar face. He would have also no reason to kill this man, Shadi Smith, if he hadn't known him.

Five Black Psyche-Locks appeared triggered by a question "Why did you kill Zak Gramarye?". For a secret, to let know of its presence, it needs to be there in the first place. There are two requirements for Black Psyche-Locks: It needs to be a suppressed memory of which secret's keeper doesn't know themselves, but there is another, an important one: Removing the locks forcibly is very likely to severely traumatize the subject. There is no way Black Psyche-Lock would appear over a simple misunderstanding.

Had fingerprints on the lighter been really Athena's, would WAA be able to prove Fulbright's cooperation with the Phantom (to which he "admitted" after discovering the forgery) and, what's more, the fact he was a Phantom?

He claimed to be Bobby Fulbright until Edgeworth arrived with the news... and then, the only topic was about the moon rock and the blood on it.

Probably not. Only two things tied Clay's murder to the Phantom: the moon rock, which no one could actually prove for a while since it was out somewhere in space, and the lighter, which the Phantom held in his possession. Though showing up to court may not have been the best idea he ever had, he'd be safe if he had taken the extra step of stopping by the museum to pick up her fingerprints. By the time the lighter was questioned as evidence, they found out it was a gun. Fulbright may have skipped over the usual protocol to verifying the validity of evidence, but without anything else to counter it, it would have passed.

The problem comes before all that, though. To even get Athena's prints on it, he'd have to know Athena would be lying unconscious in the museum. If he somehow did, he'd then have to ride along the moving launch pads to the museum, pick up her prints, and swap the pads yet again to reach that ladder and escape. However, Captain Segway, hero of the people, would have noticed the pads being swapped again. He'd then have to swap the pads a third time, so Launch Pad 1 and the museum would be in the right place. Either way, we'd be able to tie the Phantom into the case, via his psyche profile, all thanks to the photo taken just before the murder.

Then, the issue becomes "why would the killer need to swap the pads again, when he could have just leapt to freedom before the pads reached the museum?" And no, "he was hesitant the first time" doesn't count. The only reason would be that he somehow knew Athena would visit the museum that day.

But that doesn't make sense in the first place, since her visit was a coincidence. Even by the slimmest chance that he somehow got Athena's prints before the murder took place, he had to have a reason to meet with Athena, ask her to hold that lighter, and take off with it. Even he couldn't have foreseen things from that far back; Clay put up unexpected resistance and got his blood on the lighter.

Therefore, Athena's prints couldn't possibly have made it onto the lighter, and this what-if scenario is impossible.

By the time the Phantom's cover was blown, the lighter was proven to be forged evidence. The only thing left to use to tie him into the case was the moon rock, so yeah, they talked all about it.