I've seen an article shared a few times on social media entitled "Here's a twist: 91% of Americans living in Mexico are 'Illegal'". It claims:
According to a study by the National Institute of Geography and Statistics, around 739,168 thousand American citizens lived in Mexico in 2015 and, according to the National Institute of Immigration, of those only 65,302 were legal residents.
The article cites a news item in Spanish which in turn references a government poll, the Encuesta Intercensal 2015. This article does not provide any links, but I did find a summary of findings from that poll (also in Spanish). I'm not finding these figures though.
Are these actual, official Mexican government estimates regarding United States residents in Mexico with and without legal permission from 2015?