This species is known only on the basis of the type series, which consists of 11 specimens, and from which it was described in the year 1860.
The specimens are housed in only two museums in London and Stockholm.
Because of its remarkably primitive genitalia, the species is deemed the most primitive member of its genus.
No one knows where the species comes from (localities like ‘Honolulu’ = Hawai’i Islands resp. ‘Port Famine’ = Strait of Magellan in Chile seem to be questionable), it was never found again and is now considered most likely extinct. 
 Arthur M. Shapiro: Why Are There So Few Butterflies In The High Andes? Journal of Research on the Lepidoptera 31(1-2): 35-56. 1992
The classification of the Madeiran Large White is somewhat difficult, it is treated by different authors either as a subspecies of the Large White (Pieris brassicae (L.)) or of the Canary White (Pieris cheiranthi (Hübner)), or as a distinct species.
Most individuals of this insular form resembled the European mainland Large White in appearance, however the individuals, like in most species of Whites, could differ highly from each other, by their coloration as well as in their size.
The species reached a wingspan of 5,5 – 6,5 cm, it was named locally Borboleta da Madeira or Grande Branca da Madeira (in Portuguese).
The larval host plant is said to have been common cabbage (Brassica oleracea (L.)).
The entomologist R. Pinker reported in 1968 of a very unusual method of cabbage harvesting on Madeira. The lower leaves are said to have been taken away almost every day, which probably made a survival of the caterpillars sitting on these leaves very likely impossible. 
In the year 1974 the Small White (Pieris rapae (L.)) was found on Madeira for the first time, interestingly instantly in masses. 
According to a hypothesis by the entomologist B. O. C. Gardiner this new species of white, resp. a special form of granulosis virus, which was spread by this species, and against which the Madeiran Large White did not have any resistance, may be at least one of the reasons for the extinction of the endemic White. 
The last sighting of the Madeiran Large White was in 1977 (according to the European Red List of Butterflies in 1986).
 A. E. Holt-White: The butterflies and moths of Teneriffe. London, L. Reeve & Co. 1894  Rudolf Pinker: Der Lebensraum von Pieris cheiranthi HBN, und die Einwanderung und Ausbreitung der Catopsilia florella F. auf den Kanaren. Zeitschrift der Arbeitsgemeinschaft österr. Entomologen. 20 (1-3) 1968  N. Wolff: On the sudden mass occurrence in 1974 of Pieris rapae L. (Lepidoptera, Pieridae) in Madeira. Boletim Mus. Municip. Funchal, 29: 26-32. 1975  B. O. C. Gardiner: The possible cause of extinction of Pieris brassicae wollastoni Butler (Lepidoptera: Pieridae). Entomologist’s Gazette, 54: 267-268. 2003
Moroccan Green-veined White (Pieris napi ssp. atlantis)
The Moroccan Green-veined White is a subspecies of the widespread Green-veined White (Pieris napi (L.)); it was described in 1925 and was restricted to the Middle Atlas Mountains in north-eastern Morocco.
This subspecies is now considered extinct; however, I cannot find any additional information so far.
Green-veined White (Pieris napi ssp. napi (L.)); nominate race
Atlas Southern Small White (Pieris mannii ssp. haroldi)
While one of the subspecies of the Southern Small White, namely the South-Alps Southern Small White (Pieris mannii ssp. alpigena Verity) (see photo), is extending its range beyond the “Schweizer Mittelland” region since 2008 and will be certainly moving further north in the future (it actually reached my region in 2016).
Two other, relatively rare local forms are meanwhile extinct, one of form discussed here.
The Atlas Southern Small White was described in 1952, it was restricted to the Middle Atlas, Morroco.
This form is known to have been the largest subspecies.
It was last seen in the year 1973 (according to other sources in 1999) and is now considered most probably extinct.