Your lack of knowledge what happened in Finland between '39-'45 is understandable. First of all, Finland did not surrender after the winter war in Nov '39- Mar '40 - there was a peace made after the Soviet army was stopped after very heavy casualities (Soviet). Russians were the agressors, Finland lost 11% of it's land area (incl Viipuri or Vyborg). Due to these losses Finland was motivated to a new war alongside Germany to gain the area back. So in this stage I don't find any losing a was or being Finnish.
The Continuance war, Jun '41 - Sep -44, is with the game. Finland did not lose that war either, since Finland has been independent country from 1917 up to this date, which wouldn't be the case othewise. The 41-44 war ended to a peace treaty signed by the both Finland and Soviet.
Nicolas is correct, the heavy fighting continued to the mid-August, the the Soviets final cruntc was stopped. Due to the defencive win Soviets ceased to demand ultimate surrender and they agreeded on the treaty.
Interesting fact for you might be is that after the war with the Soviets Finland fought a war in Lapland against Germans to drive them away, that was Sep '44 - Apr -45, and was agreed with the treaty signed with Soviets. So in fact the Soviets did not worry about the Finland and that Germany using the Finland as a base for the northern operations as it became a problem of Finns.
One angle to the resolution of the argument between Finland and Sovits is that USA and England did not want to see Finland to fall under Soviet command due to Geopolitical reasons.
And aplogies for this long burst, I am a Finn so excuse me