What if on January 1941 Stalin ordered preparation for defensive war against Germany? How these few months could affect war?
It very much matters what sort of defense Stalin prepares for. Some choices could actually worsen the Soviet position. And even a slightly worse Soviet position could conceivably lead to the Germans winning in the East.
Better preparation and then attempting to place a strong defensive line right on the Soviet-German border (which lacked fortifications and good logistics), would have helped the Germans. Better preparation and then building up on the old 1939 border would be far better.
Whatever the Soviets do at such a late date, the German invasion will still penetrate hundreds of miles into the USSR and will have a final death toll in the millions. The Soviets will mess up and pay for each mistake in blood. However, OTL's mess ups were so huge that lessening them decreases losses and shortens the war by
years potentially.
Soviets who are better prepared to defend well back from the '41 frontier will mean that the Red Army will retain equipment and men they lost OTL (and the millions of men the Soviets suffered captured were doubly damaging, since these men could then be worked to death to feed the German war machine). That would mean that even if the Germans penetrate as deeply as OTL (so outskirts of Moscow and Leningrad), the Soviets will be able to push them back earlier and faster. That in turn means less death in the German occupied areas and a Red Army that learns faster (due to losing men at a lower rate). I've seen detailed wargames of such a scenario that ended up with the Soviets taking Berlin in late '43.
And of course, the war ending so much earlier has interesting implications all over. For example, if Germany falls to the Red Army while the WAllies are still in Italy, France might be liberated by the Resistance, not by the WAllies and DeGaule (with fascinating implications for post-war French politics). A shorter war would give the Germans less time to scale up their experiments in industrial murder, meaning many millions of Jews and other groups live through the war. A faster Soviet advance could also mean Yugoslavia is liberated by the Red Army or the Royalist guerillas, not Tito, each option leading to a very different Yugoslavia.
And an earlier end to the war also means Europe has more time to recover before the disastrous winter of 1946-1947, which not only caused mass starvation in the East, but also put the West under grueling financial pressure (the winter of '47 did enormous damage to the British financial position, as well as killing 1-1.5 million Soviets).
And if the Soviets do well enough to stop the Germans on the Dneipr, it's as the above, but even better (though I don't see Germany falling before early 1943, I don't see the division of Germany post-war as being too much different and I don't see France, Belgium or the Netherlands coming under Soviet occupation).
However, it is possible that a better Soviet performance in the war might lead to a Red Denmark, a larger East Germany and a Soviet occupation zone in Italy.
Better Soviet performance against Germany might also lead to Sinkiang remaining in the Soviet sphere - in OTL, the dictator of Sinkiang expelled his Soviet advisors and pledged allegiance to Republican China when the Germans appeared on the verge of taking the Soviet Union in late '41. If Sinkiang doesn't pledge allegiance to NatChi, then it may remain independent after the Chinese civil war ends. That in turn could also mean the Soviet Union builds up its nuclear arsenal faster than OTL during the Cold War and the Chinese (Communist or otherwise) gain nuclear weapons later than OTL (Sinkiang was the location of some important uranium mines and an important Soviet nuclear lab, which the Chinese studied when the Soviets pulled out of Northern Sinkiang).
Also, if Sinkiang remains a Soviet client, then the Soviets don't have to launch rockets into orbit at an inefficient angle to avoid overflying China.
The main benefit for the Soviets, however, is avoiding as much death as they can. Total Soviet losses due to WW2 were absolutely staggering - greater in proportional terms than the death toll caused by both Mao's crimes AND Japan's crimes in China. The loss of intelligent capable people is probably one of the reasons why the Soviet Union was never able to imagine a Socialist system that wasn't basically Stalinism, while the Chinese proved able to imagine a Chinese Communism that wasn't Maoism. A Soviet Union that suffers less death in WW2 would be a very different Cold War opponent for the US.
fasquardon