Just signed up for Reddit -- a friend forwarded this to me because I write about Königsberg/Kaliningrad. Here's a page from my dissertation/forthcoming manuscript that explains most of what you ask. (Footnotes removed, not willing to fuss with figuring out how to format those.) Enjoy!

By the time Königsberg fell in April, there had been an informal understanding among the Red Army command that the territory would no longer be German. The Polish Corridor had proven to be a political and economic disaster, and both out of the desire to punish Germany and to eliminate any future “drive to the East,” the Allies agreed that, in a turn away from previous principles of national self-determination, Germany could no longer have an exclave. The triumph of the principle of national homogeneity and contiguity would suggest that the territory be divided between the reconstituted neighbors Poland and Lithuania, and that the German populations be either assimilated or expelled to the new Germany. East Prussia first caught Stalin’s eye in August 1939, when Moscow was preparing to sign the Molotov-Ribbentrop Pact. Hitler and Stalin agreed to partition Poland and for the Soviet Union to annex the Baltic republics, creating a Soviet-German border between Lithuania and East Prussia. This shared border, combined with the historical precedent of East Prussia as a strategic ground for military action both during the Napoleonic Wars and the First World War, seems to have led Stalin to consider East Prussia a threat. That threat became a reality less than two years later, when Germany invaded the USSR. In December 1941, during a conversation with the British Foreign Minister Anthony Eden in Moscow, Stalin first introduced the idea that part of East Prussia might temporarily go to Soviet Lithuania as a reparations payment, similar to the Allied Occupations of the Rheinland and Ruhr after the First World War. As the war carried on, suggestions for provisional occupation turned into demands for full annexation. At the Teheran in December 1943, when Churchill suggested incorporating all of East Prussia into postwar Poland to compensate for Polish territory annexed by the Soviet Union, Stalin countered during the proceedings that a sliver of East Prussia should go to the Soviet Union:

"Marshal Stalin said that if the Russians would be given the northern part of East Prussia, running along the left bank of the Niemen and include Tils[i]t and the City of Königsberg, he would be prepared to accept the Curzon Line as the frontier between the Soviet Union and Poland. He said the acquisition of that part of East Prussia would not only afford the Soviet Union an ice-free port but would also give to Russia a small piece of German territory which he felt was deserved."

“All the more true” Stalin added, “because, historically speaking, this is ancient Slavic soil. If the English agree to transfer that territory to us, we will agree to the formulation proposed by Churchill.” In reality, Königsberg’s port froze quite frequently in the winter; an unspoken motive for Stalin’s insistence might have been Churchill’s earlier refusal to recognize the USSR’s 1940 annexation of the three Baltic states, leading Stalin to attempt to secure East Prussia as buffer for the Soviet Union’s western annexations. Churchill agreed to study the problem, and when Stalin repeated his request in follow-up correspondence in February 1944, Churchill responded sympathetically, assuring Stalin that he had reminded the Polish government in exile of the fact that the soil of this part of East Prussia was dyed with Russian blood expended freely in the common cause. Here the Russian armies advancing in August 1914 and winning the battle of Gumbinnen and other actions had with their forward thrusts and with much injury to their mobilisation forced the Germans to recall two army corps from the advance on Paris which withdrawal was an essential part in the victory of the Marne. The disaster at Tannenberg did not in any way undo this great result. Therefore it seemed to me that the Russians had a historic and well-founded claim to this German territory.5 In tacit recognition of Stalin’s assertion of “ancient Slavic soil,” Churchill agreed that Russia had claim to the northern part of East Prussia by virtue of having fought there before. Once again, the exclave’s future was rationalized in terms of an imagined historical claim, as ideology came into dialogue with diplomatic bargaining. At the Potsdam Conference in July-August 1945, the Allies returned to the topic of Königsberg’s future. Despite earlier informal agreements that the Soviet Union would get northern East Prussia, including Königsberg, a heated discussion broke out when Truman and Churchill suggested that in discussions about setting up a Control Commission for Germany before the final peace conference, according to the borders of the German state in 1937. The issue was that if the borders were returned, even provisionally, East Prussia would be set up as a standard Allied Occupation Zone, complete with a temporary German administration and oversight by the four Allied powers. Taken aback by Stalin’s reply, Churchill and Truman reaffirmed their plan to give Königsberg eventually to the Soviet Union, but Stalin insisted sharply that if a German administration were set up in Königsberg, even temporarily, “we’ll throw it out, we’ll definitely throw it out.” Churchill and Truman ultimately agreed that Königsberg would remain under Soviet control for the time being, but insisted that the final discussions of status and borders be determined in the formal peace treaty. As cooperation broke down between the Allies, that treaty never materialized, however, and Königsberg’s provisional status became permanent. The southern two-thirds of East Prussia, including the cities of Elbing, Marienwerder, Deutsch-Eylau, Bartenstein, Rastenburg, Allenstein, Johannisburg, and Soldau, were incorporated into Poland, and the Memel Region, north of the Memel River, including the city of Memel, were folded into the Lithuanian Soviet Socialist Republic. The remaining territory, including Königsberg and the Samland Peninsula, and the towns of Insterburg, Tilsit, Pillau, Cranz, and Gumbinnen, fell to the Soviet Union, and was formally annexed on 17 October 1945.