To quote from your website:
When I began my own research the prevailing understanding was that Aristotle had rejected the story of Atlantis as an invention. Franke’s study has turned this idea completely on its head, clearly demonstrating that there is implicit evidence that Aristotle was “rather inclined towards the existence of Atlantis”. However, he goes further and forensically demolishes the idea that the two passages in Strabo’s Geographica (2.3.6.& 13.1.36) were quotations from Aristotle and even if they had been, they were references to Homer not Plato.
So, being a scholar, I looked up Strabo's geography on a site that had the original text along with an English translation. This is the one I used:
Atlantis is NOT mentioned in Geographica 13.1.36
However, the Naval Station, still now so called, is so near the present Ilium that one might reasonably wonder at the witlessness of the Greeks and the faint-heartedness of the Trojans; witlessness, if the Greeks kept the Naval Station unwalled for so long a time, when they were near to the city and to so great a multitude, both that in the city and that of the allies; for Homer says that the wall had only recently been built (or else it was not built at all, but fabricated and then abolished by the poet, as Aristotle says); and faint-heartedness, if the Trojans, when the wall was built, could besiege it and break into the Naval Station itself and attack the ships, yet did not have the courage to march up and besiege the station when it was still unwalled and only a slight distance away; for it is near Sigeium, and the Scamander empties near it, at a distance of only twenty stadia from Ilium. But if one shall say that the Harbour of Achaeans, as it is now called, is the Naval Station, he will be speaking of a place that is still closer, only about twelve stadia from the city, even if one includes the plain by the sea, because the whole of this plain is a deposit of the rivers — I mean the plain by the sea in front of the city; so that, if the distance between the sea and the city is now twelve stadia, it must have been no more than half as great at that time. Further, the feigned story told by Odysseus to Eumaeus clearly indicates that the distance from the Naval Station to the city is great, for after saying, "as when we led our ambush beneath the walls of Troy," he adds a little below, "for we went very far from the ships." And spies are sent forth to find whether the Trojans will stay by the ships "far away," far separated from their own walls, "or will withdraw again to the city." And Polydamas says, "on both sides, friends, bethink ye well, for I, on my own part, bid you now to go to the city; afar from the walls are we." Demetrius cites also Hestiaea of Alexandreia as a witness, a woman who wrote a work on Homer's Iliad and inquired whether the war took place round the present Ilium and the Trojan Plain, which latter the poet places between the city and the sea; for, she said, the plain now to be seen in front of the present Ilium is a later deposit of the rivers.
He does mention Atlantis in 2.3.6 but it appears that Francke is attempting to tie the mention there with the section that does NOT mention Atlantis solely on the discussion of the city of Troy. If you read the whole chapter, it's clear that he's talking about Troy in Chapter 13 and that Atlantis never comes into it.
If you read all of Chapter 2, Aristotle is talking about how to tell real geography from fanciful tales. Aristotle says that the subsidence of land is known and uses the idea that Atlantis sank to support the case for "land sinks under the ocean sometimes." Aristotle says directly "Poseidonius thinks that it is better to put the matter in that way (i.e., "Solon said that Atlantis sank under the waves") than to say of Atlantis: "Its inventor caused it to disappear, just as did the Poet the wall of the Achaeans."
In other words, Aristotle's opinion is that his source (Poseidonius) has made a lot of mistakes in his books, and that rather than trying to explain "why we can't see Atlantis", Poseidonous did a nice job of explaining away the fiction -- just as Homer had a wall get swept away by the sea (a nonexistant wall that was keeping out Greek ships -- made for a great story but it was pure fiction.)
So no, he never says Atlantis is real.
And this is the problem about people using "a sentence here, a sentence there" as evidence.
You have to read the WHOLE chapter.