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I believe that only God is eternal and immortal by nature and in essence. The angels and the souls of men are immortal only because God bestows this immortality upon them by grace. If if were not for the immortality which God bestows by His divine will, neither the angels nor the souls of men would be immortal of themselves.
Men's souls have no pre-existence. The how of the soul's birth, as well as separation from the body at the moment of the latter's biological death that it might be reunited to the body when the dead are raised at the Second and glorious Coming of our Saviour is a mystery which has not been revealed to us.