How did the concept of Heaven and Hell become a Christian doctrine?

The concept of heaven as a place of reward entered Judaism at the time of the Babylonian Exile, very likely from the Zoroastrian religion of the Persian liberators, and thus became part of Christian doctrine. The Persian concept of hell as a place of punishment was eventually rejected by the Jews, but was resurrected as part of Christian belief. This might have been from residual elements of belief in the concept among some of the Jewish population, or it might have been the result of continued contact with the Persians. We know from the reference to Zoroastrian priests, or magi, in Matthew's Gospel that early Christians were well aware of Zoroastrianism.