So she gets a call from "Amazon", who forwards her to the "FTC", who forwards her to a "CIA agent". Everything else aside, how the fuck do you think some random Amazon customer service rep is 3 steps removed from the CIA?
Devil's advocate: target has a forensics team that frequently collaborates with the FBI, so a developed relationship leading to an easy transfer like that isn't too crazy
The premise was the identity thieves were involved in international drug trafficking, so in that sense CIA involvement is plausible if you don't look too hard
FYI to all Hexbears, most government agencies, especially federal ones, will not call you first. They send paper document via mail letting you know what the deal is before anyone even attempts to contact you via phone. So if you ever get a cold call from the IRS, FTC, or CIA, it's not actually them.