ONE correction : Stalin did not want the former territories of the Russian Empire, but only some of them : before 1914 the biggest part of Poland ,including Warsaw,was a part of the Russian Empire,but Stalin wanted only the Eastern part,because he knew that Poland was a poisoned chalice for the USSR and that even the communist Poles were hostile to the USSR . He preferred that ''fascist '' Germans should occupy ''capitalist '' Poles .The Molotov - Ribbontrop Pact sealed the fate of Poland and the Baltic states. Hitler wanted Lebensraum in Poland, Stalin wanted the former territories of the Russian Empire. To say that the Soviets and Germans didn't coordinate the invasion of Poland is simply not tenable. The sectors to be occupied by each invader had been agreed upon before the invasion. German forces that had pushed beyond the agreed upon boundaries withdrew when the Soviet forces arrived, and turned over prisoners. Eastern Poland was territory incorporated into the nascent Polish state following the Polish - Soviet War of 1919-21, and was predominantly populated by Ukrainians, Jews, and Belarussians. Perhaps this is why the Western Powers did not strenuously object to Stalin's takeover, as this territory was not part of the original Polish state created in the Treaty of Versailles.
About the coordination of the Germans and Soviets : the Germans did not know when the Soviets would invade, because the Soviet attack was depending on the success of the German attack and on the failure of the Wallies to be in Berlin on September 15 .If after the German attack,there was a coup of the German generals and the French were advancing to Berlin, Stalin would not move .