According to a former CIA director Oswald was working for the Soviets. Krushev wanted JFK dead but killed the hit some time before.
Oswald did it anyway. That’s according to Eastern European intelligence agencies at the time.
If he was working for the Soviets it’s strange that his last phone call would be with his contact in U.S. counter intelligence.
If I remember my research correctly, wasn’t that around the same time Khrushchev got caught with his pants down in West Germany when the assassin he sent in to kill defecting communist party members got caught and ended up having a medal personally given to him by Khrushchev among his belongings?