https://www.archives.gov/files/research/jfk/releases/docid-32114512.pdf
States that it was TERESA PROENZA, the cultural attache for the Cuban Embassy, who first greeted this man who walked in "cold"...
The point here is that TERESA does not speak English so she turned him over to the nearest person, higher in rank, who spoke English...
Except the calls on Sept 27th were in SPANISH - adding more strength to the notion it wasx not Oswald on the 27th... and we know about the 28th...
DJ
https://www.archives.gov/files/research/jfk/releases/docid-32185802.pdf
Mora makes the comment that they can only link OSWALD to Mexico is by his activities BEFORE he went to Russia.