I have yet to complete the Looming in the Shadows special research, and have just acquired the Super Rocket Radar to give you access to Giovanni. When this research was first introduced, the Shadow Pokemon you were given a chance to catch after the battle was Articuno.
New Special Research quest were given monthly afterwards before COVID-19 lockdowns. The Shadow Pokemon at the end of each of these battles changed to a different legendary (Zapdos, Moltres, Raikou, Entei in that order).
With the current Go Fest Battle Challenge, Giovanni's Shadow Pokemon reward is Suicune. I have already caught it from the Go Fest's Super Rocket Radar.
I have heard that Giovanni's legendary Shadow Pokemon changes based on the month, but I am not sure if this is specifically because of the month, or because of the research quest that rewards the Super Rocket Radar. So I'm asking which of it is these, and if I were to use my Super Rocket Radar from the Looming in the Shadows research, would Giovanni have Articuno or Suicune? Of these two, I would prefer to receive Articuno.
Best Answer
The shadow legendary Pokémon Giovanni has is based on the month, not when you received the quest. So you would get another Suicune and not Articuno.
It does not matter how you obtain the Super Rocket Radar (whether it be from the Looming in the Shadows or the Go Fest challenges), you will battle and catch the last legendary Pokémon Giovanni was in possession of.
When the Looming in the Shadows quests were active every month, I missed the first three months and never was able to complete the quest. When I was finally able to defeat Giovanni for the first time in February 2020 with the original Looming in the Shadows quest I received in November, the legendary reward was Raikou.
This happened again a few months later. When I completed the Looming in the Shadows for Feburary, I received the quest for March but was unable to complete the quest until May. While the quests were temporary discontinued in April, I received March's reward for completing it May (that reward being Entei)