I think the animagus match the patronus in this case

Most people, when they become Animagi, have an Animagus form that matches their Patronus if they know how to produce one.

Patronuses always match the animal form of the Animagus.

Always? Can't they differ?

Maybe they can differ. Tho I can't think of a single person having different ones. Is there anyone?

Lupin: Wolf x2

Minerva: Cat x2

Morrigan: Crow and not known patronus

While Patronuses can change due to trauma, obsession, love, or grief, I don't think there's a single canon example of a Patronus not matching an Animagus' animal form.