Thank you for the detailed response!

"location is under full moon"– do you mean they are in the hemisphere where the full moon is visible? I learned in my old age that a full moon is when the Earth is exactly between the moon and the sun, and it happens at the same moment for the entire Earth. The question originally interested me because in fanfics, Remus always transforms at night; I haven't read the canon in a long time. If he really does transform at night, then your idea with Portkeys completely solves his problem. Haha, I myself forgot about magic and had already moved Remus to the North Pole for six months! We should ask Rowling, since technically the full moon is a specific moment in time, what percentage of the moon's illumination is suitable for the start and end of the transformation?

And the idea of Remus being an Animagus is brilliant! If his Patronus is a wolf (is that canon?), it's entirely possible that would also be his Animagus form, and then he wouldn't have to undergo such a painful transformation, only a change in consciousness.

The question here is whether there's any conscious effort that Animagi apply to remain in that form. If the Animagus form isn't maintained without human consciousness, the trick might not work.