Of the philosophers, Thales is vaguely reported to have taught that souls are immortal. But neither he nor his immediate successors... believed in the immortality of particular souls... This doctrine belongs to the Orphic tradition. In Heracleitus and Parmenides we find the two doctrines of immortality... implicit in mysticism, separated... for the first time. Heracleitus is the champion of the Dionysiac... life and death... in an unending cycle; Parmenides, under Orphic influence, teaches... Soul has fallen from... light and reality to the dark and unreal... bodily existence. This, however, is... only 'the way of opinion'... [Parmenides] feels.... that... substantiality... is not so easily got rid of. But he will not give up... eternal substance. The most interesting fragment of Parmenides... seems to enunciate, for the first time in Greek thought, the mystical doctrine of eternity as a timeless Now, as opposed to the popular... unending succession. 'There remains then only to give an account of one way—that real Being exists. Many signs... showing... it is unborn, indestructible, entire, unique, unshakable, and unending. It never was, and it never will be, since it is all together present in the Now, one and indivisible.' Empedocles... repudiates... Parmenides, probably on the ground that he reduces the world of time and change to nullity... thus leaves no pathway from appearance to reality. His doctrine of the soul’s exile and wanderings is... Orphic doctrine, which Pindar also gives... in the second Olympian Ode. The Soul sins by separating itself from God... from love and a choice of ' strife ’ in the place of harmony. The immortal Soul is... love and strife blended; the body... only an 'alien garment'... perishes at death. ...Empedocles describes the Soul as a ratio, or harmony ...the complex of...'strife'... bound... by the principle of unity...'love'...Parmenides ...may be ...rejects the Pytdhagorean doctrines ...finds truth in static materialism.
source
William Ralph Inge, Philosophy Of Plotinus: The at St. Andrews, 1917-1918 (1918) Lectures XII, XIII Immortality of the Soul, Vol.2, [https://archive.org/details/in.ernet.dli.2015.533523/page/n17/mode/1up?view=theater pp. 3-5.]