Title: A Fate that Returned to Fire

Mouri and Banba sit on some chairs and discuss the situation.

Mouri: "The hairbrush...did you ever let anybody else use it?"
Banba: "I don't think so...I've been living with Hatsune for about half a year now. Although maybe some detective might have used it whilst I was out..."
Amuro: "I have never been inside your house!"
Banba: "The fact that you're a detective makes you suspect...if you're skilled enough to dodge the guy I hired... then when you came to my house, you could've taken some of my hairs off the brush and replaced it with somebody else's and then put the guilt on me."
Amuro: "Ah..no, I wouldn't ever do such a spy-ish sort of thing..."
Megure: "I'm afraid you're wrong in any case. I just received the results from forensics. The hair on the hairbrush is definitely Mr Banba's."
Amuro: "So that means that..."
Takagi: "Permission to escort you to a police station?"
Banba: "Fine!"
Takagi: "I've parked the car a little bit far so you'll need an umbrella, or else you might get wet..."
Banba: "It's raining again?"
Takagi: "Yes...quite heavily..."
Banba: "I don't mind getting a little wet."

They start to make their way out. Conan puts Mouri to sleep from under the table.

Mouri (Conan): "Are you sure about all this? Banba? Did you really..."
Banba: "Well what can I do? It's come to this so I'll just have to show I'm innocent at the station..."
Mouri: "I see...in which case...you are not the murderer!"
Amuro: "Eh?"
Megure: "Oh come off it, Mouri..."
Mouri: "Recall this...in terms of doors going out into the carpark...there was also a way via the toilet window... in which case the only way to go is by the front door...somebody would have certainly seen if he, Banba, the main man of the show, went out that way."
Amuro: "It might be the case that it wasn't that he wasn't seen, just wasn't noticed. He could've disguised himself in the toilet, if he'd hidden his clothes in their beforehand... like, a knitted cap or a long windbreaker..."
Banba: "What about the phone call before the explosion? She said "Goodbye!"
Amuro: "Did she really call you just before the car caught fire? Maybe what actually happened was that - "
Banba: "That's all just words! Hatsune really did... Check her phone!"
Takagi: "Well we could put back together the data but a whole conversation - "
Megure: "And these clothes that were used for the disguise?"
Amuro: "He could have flushed them down the toilet by cutting them into lots of tiny pieces with a pair of scissors and a knife..."
Mouri: "What about shoes? You can't easily cut up those..."
Amuro: "He wouldn't need to change those! If he kept on walking in them then it wouldn't make any difference anyway."
Mouri: "The shoes are evidence that he is not the murderer."

Takagi looks at the soles of the shoes that Banba had taken off. There's cream from the cake in its grooves.

Ran: "Because he trod on the cake..."
"When?"
Ran: "Before Hatsune left the shop."
Takagi: "If he'd walked on the wet pavement...Especially if he'd been in a hurry to get back into the shop once he'd set the car on fire!"
Megure: "So, do you say that Banba never went out of the shop..."
Mouri: "I thought it was trick that he'd pulled off at first. I thought, by some way or other, he'd changed his shoes...but the cake in question was some that this here young detective dropped and then got trodden on just by chance... Banba never mentioned the cream on his soles to me...he is even now willingly leaving the shop into the rain outside, risking his previous 'evidence'...That is how I realized that the cream isn't a part of a trick...it is real affirmative evidence that he is innocent."
Amuro: "But, but, what about the DNA? On Hatsune's false nail - "
Mouri: "Couldn't it have been her own skin?"
Amuro: "What...what are you saying? Two people would have to be relatives otherwise a close match would indicate...In any case, women don't have y chromosomes, so you should be able to work things out quite quickly!
Mouri: "The fact is, the skin had been corrupted with all the mud and the rain...it could be that because the sex chromosomes were indiscernible."
Amuro: "But even still...that the two of them...coincidentally..."
Mouri: "Their meeting might have been a coincidence...but what drew them together might have been necessity, because they were twins..."

Mouri talks about the hotel fire incident. Amuro explains about monozygotic but dual gender identical twins. He hears from Banba that her height was around the higher 140s.

Amuro: "In the case of monozygotic (identical) opposite sex twins, the female has Turner's syndrome and so is prone to shorter statures."
Banba: "But...why was there her skin on the ends of the nail?"
Mouri: "When she'd heard you were rescued from the same fire, she said, 'I'll investigate that myself'. The only conclusion possible is that she would use DNA sequencing to find out if you two were twins. We could surmise that when she got out of her car, she got a call from the company with her results...there was no way they could get married...being identical twins... The skin on the false nail was probably a result from her scratching her tearing at her face as she cried, to such an extent that the nail fail off...it fell into the umbrella that she'd dropped and was blown away...and that we're now investigating and awaiting the results of."

Megure gets a phone call
Megure: "Apart from the sex chromosomes the others matched Banba's exactly and it also fitted the DNA from the corpse." It is confirmed that the DNA is hers.
Takagi: "So it was suicide..."
Megure: "The timing of the company was pretty bad."
Takagi: "They heard it was the wedding tomorrow, so they probably wanted to get in their news as quickly as possible...before it was too late."

Conan narrates.
Conan: "Banba's cry cut split through the rain and echoed all around...it wasn't clear why she had chosen to die by fire... perhaps in order to restart everything she'd wanted to go back to the beginning...into the midst of the flames that set the pair of them towards this fate..."

The next day

Amuro works part time at Poirot, and asks to be made Mouri's apprentice.

Amuro: (whispers in Mouri's ear) - "As tuition fees, I was thinking of paying about................per case...."
Mouri: "Are you serious?! Indeed! In which case, young Amuro, call me, "Master Mouri"!"
Amuro: "Yes, sir, Master Mouri!"
Conan: "And here's another troublesome one..."