Eternal Life is Immortality, whether here on earth or on another plane. Immortality is essentially Escaping Death, Unending Existence, Exemption From Dying. For After death if we live on, then we still haven't escaped death, but lived on in another form. A metamorphosis of being. Does this still constitute Immortality
Continuing Indefinitely throughout Existence with no stoppage of life or consciousness this is really Immortality in its truest form. If the body dies and the soul lives on, or if the body dies and somehow the 'body' lives on, then is this Immortality.
Even though there was death in the equation?