For what it is worth, here is Prof. Jean-Claude Larchet's treatment of the question in one of the later chapters of his book 'Life after Death according to the Orthodox Tradition' (with minor typographical errors corrected & sans scriptural, patristic and other references, as I regret I cannot bear even thinking of transcribing all of the footnotes!) Hopefully, it helps.:
"THE QUESTION OF THE APOCATASTASIS. The foregoing objection and response allude to a subject debated long and hard in the Church: the apocatastasis.
The theory of the apocatastasis (that is to say the universal restoration to a primal state) was chiefly defended by Origen and by the so-called 'Origenist' current. It was also upheld by St. Gregory of Nyssa, but under a more temperate and ambiguous form to such a point that his position could be interpreted in an orthodox sense by some ancient and modern authors. It has likewise tempted, under various forms and in different eras, certain Christian thinkers to whom the idea if an eternal hell seems incompatible with God's sovereign goodness.
According to this theory, hell is not eternal; all those confined there, including the devil and the demons, will be ultimately saved and glorified.
This theory has remained however quite marginal. It has given rise to critiques by numerous Fathers, before and after having been officially condemned by the Church, along with all the other Origenist errors, during the Fifth Ecumenical Council (Constantinople II) in 553.
With the exception of Origen and his disciples, all the Fathers teach the eternity of the pains of hell and the eternity of the condition of those who will suffer them.
One of the chief objections voiced to the assertion of hell's eternity is that the latter is incompatible with the existence of a good and merciful God. However, the origin of hell is not, as we have seen, God's will, but the will of the devil, the demons and certain people. Hell, like evil, is not a positive ontological reality; it has only a privative existence; it exists for those subject to it only as the absence of the benefits of the Kingdom, only because of a rejection of God. By this very fact it has not been created by God. As for its eternity, it follows from the possibility of the devil's, the demons' and men's free choice to persist in evil and reject right to the end God's eternal and uncreated grace. Bessarion of Nicæa affirms: "The justice of eternal punishment becomes apparent above all in the irrevocable disposition of the unruly will of sinners, for to the will's eternal perversion is due an eternal punishment."
This argument from angelic and human freedom, upon which the goodness of God refuses to impose itself because He respects it right to the end in its choices and their consequences, the worst included, has been brought to the fore by several Fathers, St. Maximus for one, and logically follows moreover from the previously explained notion of hell.
Two objections remain: 1) how can it be asserted that hell will exist as a continuation of Hades, whereas nothing is final concerning the future of those abiding there before the Last Judgment? 2) how can we, a priori, consider the choice of those found in hell to be final?
As to the second objection, it must be recalled that a person no longer has the possibility of repenting or modifying his choice not only after the Last Judgment, but after the moment of his death, and that, between the moment of death and the Last Judgment, it is only the prayers of the Church, the saints, and the other faithful who are able to obtain from God a change in his condition. That surely limits the freedom of a person, but we know in advance that out freedom will be limited in this way and must make our choices accordingly. The warnings of the Fathers are, moreover, aimed at this, and this is also one of the teachings of the Gospel parable of poor Lazarus and the wicked rich man.
To the first objection we reply that the affirmation of the eternity of hell rests on the teaching of Christ Himself. This teaching rests on the foreknowledge He has, insofar as God, about what the future life will be.
The rejection of the theory of the apocatastasis does not prevent the Church and its members from praying that all might be saved. But there is a twofold difference between this attitude and adherence to the theory of apocatastasis. On the one hand, the latter affirms the certainty of universal salvation, while the former only desires it, wishes it, hopes for it, without having any certainty that this will be realized. On the other hand, in the present situation – and this being until the Last Judgment – the condition of no one abiding in Hades can be seen as absolutely final. Therefore it is perfectly legitimate to hope for the salvation of all and to pray to God for this to be realized."
Of course, this chapter really needs to be digested within the full context of the book (with scriptural and patristic citations intact) since it provides much necessary background on Patristic anthropology and teachings concerning the intermediate state between death and the Last Judgment, as well as teaching on what heaven and hell actually are (i.e.: states of being- relative to God and his grace, as well as in relation to one's neighbors and to one's self made in the Image of God- as opposed to literal places.)
But from the sounds of it, your interlocutor would not be convinced by the testimony of the Fathers and their exegesis of scriptures and would perhaps demand evidence from scripture alone?