Queen Veranke joined the Avengers in Jessica's image in New Avengers (1st series) #3. The real Jessica Drew joined the team in #48.
Jessica Drew originally lost her immunity power in Marvel Two-In-One #85, and her bio-electric bolts after her death and resurrection in Spider-Woman (1st series) #50 and Avengers (1st series) #240-242. Her full powers were restored in Sensational Spider-Man Annual '96, but stolen again in Spider-Woman (3rd series) #1.
She was replaced by the Skrull Queen Veranke for New Avengers (1st series) #1-47 and all other comics from that period, leading to her return in Secret Invasion #8.