The cycle of the Shadow Birds continues in Pokémon GO. May has begun, which means that Shadow Zapdos is out and Shadow Moltres has taken over as Giovanni's third-slot Pokémon. After you do battle with the Team GO Rocket's boss, Shadow Moltres will now be the encounter. However, if you missed Shadow Zapdos, don't fret… it's coming back for a special period of time after Moltres' run in May. Here are the full details.
Originally, the plan was for Shadow Articuno to be the Giovanni encounter for March, Shadow Zapdos to be the Giovanni encounter for April, and Shadow Moltres to be the Giovanni encounter for May. The Legendary Birds of Kanto would essentially take up the entire Team GO Rocket plan for the whole of the Season of Legends. However, then April happened. Pokémon GO introduced an update in April that essentially broke Team GO Rocket balloon encounters. As a result, Niantic removed Team GO Rocket from Pokémon GO for almost two full weeks.
Team GO Rocket was added back to the game before April closed out, but Niantic has decided to feature Shadow Zapdos again for a short period of time in June 2021 for anyone who missed out on it due to the April mishap in Pokémon GO. Moltres will remain Giovanni's third Pokémon and the encounter reward throughout May, with Shadow Zapdos taking over once again on June 1st, 2021 at 12 AM local time. It will remain in the game until Thursday, June 17th at 12 AM local time. We currently have no information on what will take over or if there will be a new Team GO Rocket research for Zapdos in June.
I tend to think that there will not be a new Team GO Rocket research for the re-release of Zapdos. The April Timed Research rewarded the Super Rocket Radar meant for Zapdos, and next week's Luminous Legends Timed Research will reward the Super Rocket Radar meant for Moltres. Most likely, Niantic will expect players who missed Zapdos to use their April Radar for Moltres during May and then save their May Radar for Zapdos when it returns in June. Who knows, though? Maybe they'll be generous and throw us another Radar. When we know, Bleeding Cool will be on deck to report.