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It seems that records from the early period can be very patchy.
http://www.argbrit.org/ does show a marriage of a Catherine Alais in 1824, a native of St Giles, London, witnessed by John Alais, a burial for a John Alis/Alais, aged 72, in 1847, and of a Jane, aged 72, in 1853.
There is also a book on google books, "Travels in Buenos Ayres and the adjacent provinces of the Rio de la Plata" from 1828 which mentions
Two sons of Mr. Alais, an engraver and mechanic of considerable talent, well known in London
https://familysearch.org has a few records as well.
