AskHistorians

While the Axis did some minor coordination, the Allied powers definitely coordinated on the strategy of handling both wars at once. There was an agreement to prioritize Germany over Japan as Germany was the more immediate existential threat to the Allies. These agreements included American and British commitments to opening additional fronts in Europe and Soviet commitments to opening additional fronts to Japan.

That said, the was some separation of the Axis. For instance, while Germany declared war on the USA after Pearl Harbor, Japan did not declare war on the Soviet Union following the German invasion of the Soviet Union due to a peace treaty between Japan and the Soviet Union. This is important as Stalin used his Far East troops as part of the Soviet counterattack of the German invasion. Japan hoped this peace treaty with the Soviet Union could be used to negotiate a conditional surrender. This didn't work; the Soviet Union declared war on Japan between the dropping of the two atomic bombs.