A very interesting scenario and one that gives the illusion of throwing of the balance of power. In 1941, Germany had already invaded France and was at war with Great Britain. The US was supplying Britain with logistical and military support. By Germany declaring war on Japan along with the US and Britain, it did not change the course in the European war. Hitler's declaration of war would be in name only because how was he going to contribute to the fight against Japan? Much in the same way as Mexico declaring war on Germany. Very little military effect.

Now, this would make it difficult for Roosevelt to declare war on Germany since there was no reason to. But, sooner or later there would have been a Lusitania incident and the US would have its reason to declare war on Germany. Hitler knew the US was provided protection for convoys destined to Britain and his patience would have worn thin to the point that he might even allow the U-boats to attack such US protection.

In the end, nothing much would have changed.

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American by birth, TEXAN by the grace of GOD!