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This is both stupid and at the same time a slanderous straw man, attributing the opinion that anyone "definitively exclude(s) the possibility of their conversion" to anyone here.  Absolutely NO ONE does this, nor did the poster to whom you were responding here.

What is this emotional drivel that you're trying to pass off as theology?

Entire point of the teaching from Pope Gregory XVI on that other related thread is that while this is possible, unless the distinctions are explicitly made, the general act of "praying for" a departed heretic undermines the Church dogma regarding EENS.  It's incredibly unlikely, and St. Alphonsus said that the chances were miniscule, for someone who lived either outside the Church or in sin their entire lives, to experience a last moment conversion, since that's not how God's Providence normally works.  But no one holds that it's not theoretically possible for this to have happened and definitively excludes the possibility.

Church presumes them lost, and in the external forum treats them as lost.  If we die and go to heaven, and happen to find that such a one was saved in their last moments, then glory to God.  But to try to spin this as if it's something likely or common, or to indiscriminately, without making all these distinctions, claim to be praying for them, is to express the sentiment that there is good hope of their salvation, even if they did not convert to the Catholic faith in their last moments.

There was a decree of the Holy Office under Pope St. Pius X, in response to a question about whether Catholics could say it was possible for Confucius to have been saved, and answer was that Catholics must respond that he was damned, as all infidels are damned.

Bottom line is that the people who speak this way, as you do, don't REALLY believe that there's no salvation outside the Church.  You pay lip service to the dogma because you have to ... after all, it's a dogma.  But that's as far as your belief in it goes.

If St Thomas knows nothing of BOD or BOB in his "Catechetical Instruction", he clearly teaches it in the Summa, did you not read my earlier post?

No, I do not hold that someone can have BOD without faith. But I do hold as absolutely certain that God desires every man to be saved, and that he gives every man the grace to save his soul. The conclusion is obvious. God is not limited by the ordinary means He established for salvation, He sees the heart, and the Almighty acts directly on souls. Faith usually comes by hearing, yes, that is the ordinary way, but with some, it is clearly impossible. Were they then created for damnation? Just a simple yes or no will do.