He might know where Shadow Stalker goes to school. Armsy does tend to get over-focused from time to time.
Okay, minor spoilers? Coil set this up. Pulled strings to get Taylor shoehorned back into Winslow. Sent Armsmaster an anonymous message about how if he hears a call for the fire department for Winslow, it's Taylor going nuts there.
Armsmaster has sunk enough time and effort into recruiting Taylor (and been humiliated by her, and seen how powerful she can be) that he can't not respond to this.
If he can recruit her, and train her up to be powerful enough to help him take out an Endbringer, his reputation will be forever stellar. (So he thinks). [After all, she's already far more powerful than Dauntless ...]
Coil has set the whole thing up with the expectation that it will blow up in the PRT and Protectorate's faces. Make them look bad, just by pulling a few strings and pushing a few buttons.