Hm, I'm guessing the Ameri-Jazz swap started in chapter 407, when Jazz ran into Ameri. For this arc, Jazz used his double-agent status rather masterfully. Given his own bloodline magic, it isn't impossible that he used the same Loki transformation on Ameri and Ameri enhanced it a bit more with the glasses and her own romanticism bloodline.
- In chapter 407, Jazz revealed that cased the place by working at the museum before the start of this arc and his brother confirmed Jazz's intel gathering role in chapter 410.
- While chapter 408 was going on, Jazz likely confided to Ameri and co that he is a double agent but he wants to get back at his brother Malus for his abuses. Due to the difference in fighting strength, Jazz likely recongized he can't stop Malus while Ameri can. But in order to bring Ameri into a direct confrontation with Malus, they must remove the means Malus has at confusing them while also eliminating his escape options. In chapter 410, we saw that Malus (his brother) didn't leak his escape plans until the very last moment. Jazz likely foresaw that Malus planned multiple escape routes as it is impossible to intercept him ahead of time. So Jazz likely told Ameri that she must impersonate him and follow Malus and ambush him when he least expects it.
- In 409, it is important to note that Jazz's impersonation of Ameri did not show off any superpowers - he merely landed in front of Malus in a magnificent bluff. Compare his impersonation to Ameri's actual ambush of Iruma in the earlier chapters (between 399 and 401) and that should have been a giveaway. Also, Jazz likely tied his familiar to the key as a backup while Ameri waited beneath the pile of gold. Jazz's familiar ensured the key can be tracked in the middle of it all that mess. Meaning even if Ameri was caught up with the transformation/misdirect earlier, she can find Jazz's familiar for the key.
Ameri will likely pass her scala exam with flying colors in this arc and move up a rank (or half a rank, thanks mephisto). As for Iruma... well, I predict Ali may have something to do with the key. Otherwise at the very worst, he did give Mephisto another amusing experience and he moves up a quarter rank.
Jazz is the real hero/MVP in this seeker-stealer arc, even if he is not the focus. And I expect him to get promoted after all this.