Sakhalin island was divided between Japan and Russia up until World War I, with the Russians in the north and the Japanese in the south. After the Bolshevik revolution, Japan occupied Northern Sakhalin between 1920 and 1925. They gave the island back to the Soviets in return for being allowed a portion of the oil from the oil fields in Northern Sakhalin.
What if the Japanese had established a White Russian puppet state in Northern Sakhalin instead of giving it back? They were under quite a bit of pressure from the US and Europeans to stop meddling in the Soviet Union, but they did have White Russian allies who could have used a base of operations and full access to the oil would have been a help to the oil-starved Japanese, though it would have provided only a fraction of the oil they needed.
A white Russian state in Northern Sakhalin would have been a tough, lonely place. The northern part of the island is subarctic--not a fun place to live. It would have had a small population, probably no more than half a million at most even with the die-hard exiles. The strait between the mainland and the island is narrow. It sometimes freezes over in the winter. The White Russians would have been almost totally dependent on the Japanese for whatever independence the Japanese would have let them have.
So as of the lead-up to World War II, the Japanese have a White Russian puppet state in Northern Sakhalin and access to enough oil to supply in the low double digits of their needs. What, if anything, changes?
My guess: Not much. The White Russians get crushed by the Soviets in August 1945. That's the obvious way to vote. Anyone with a more creative take on what would happen?