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Minerva McGonagall's Animagus form is a cat. Her Patronus is also a cat. We know that James Potter was a stag Animagus, and his Patronus was a stag as well. I'm not sure if Sirius Black's Patronus ever appeared in the books, but I am pretty much sure it would have been a dog.
Is the form of an Animagus directly related to the form of a Patronus?
Just to clarify, in an instance that the Patronus changes (as it is established by canon), does this mean that the Animagus form also changes? Or is it impossible for both to change for an Animagus?