This is news to me friend . I have never heard of a difference between Eternal Life and Immortality. I always believed it to be the one and same thing.
As far as I understand scripture Adam never had either. He was not created as an immortal soul - when God breathed into him the breath of life it was human life (not et.life) and he became a LIVING SOUL (not an eternal living soul). Adam would have become immortal /eternally living if he had obeyed God and chosen the right tree God had commanded him Gen.2v16,17. In Ezek.18v4 we read that the soul (a living person) that sins shall die.Job says that man is mortal. 1Cor.15v45 the first man Adam was made a living soul; the last man (Jesus) was made a quickening spirit. A different life in each from the start.
Trad.christianity believes in Adam's and all men's immortal soul which has no scriptural support. ETERNAL LIFE / IMMORTALITY is a GIFT from God - no man (apart from Jesus ) is born with it . The HS of God is required for that and is given only to the obedient Acts 5v32. Adam was not obedient and did not have eternal life or immortality.
This is my understanding of scripture.
Right. Adam was Not created with an immortal soul.
Angels were not created immortal either. Angels can sin.
Adam was not offered immortality [death proof]. Adam was offered eternal life or everlasting life. In other words, Adam's life was conditional. Adam could continue to live in healthy human perfection of mind and body as long as he breathed and ate, etc. and obeyed God.
Those that put on immortality [1st Cor 15vs53,54] are the ones called to heaven to rule with Jesus for a thousand years.
Earthly subjects of God's kingdom going back to Abel will have eternal or everlasting life as Jesus promised. All those making up the promise to Abraham that all families of the earth will be blessed, and all nations of the earth will be blessed [Gen 12v3; 22vs17,18] will be blessed with healthy human perfection of mind and body with endless life on earth as long as obedient. By the end of Jesus millennial rule over earth all living ones will have chosen to be obedient to God's way of ruling.