I've encountered the same problem previously experienced by players regarding this quest and am unable to finish the quest as reported previously.
Quote - The1Kobra
"In the latest patch, it's currently impossible to complete this quest. I've spoken to Annie after clearing Caer Lem but she will only talk about the scavenger business, not this sidequest.
I've attempted to wait for the scavengers to clear Caer Lem, but Annie still won't talk about her quest after that."