Pino,
"Pastiliére...some believe it is of Italian origin and was taken to Japan where the Portuguese brought it back"
It's the other way around. It's most likely a fig of Portuguese origin. A very old variety known in Algarve as Figo Preto Temporão.
Among many other things (like firearms), the Portuguese took fig plants to Japan ( they reached Japan in 1542) in their voyages during the 15th and 16th centuries. A couple of centuries later, the Italian/French "discovered" them there and brought them back to Europe.
The correct information is in this website, a link that Francisco has already posted:
http://www.planetfig.com/cultivars/fcveng8586.html
"The origin of this fig tree remains doubtful, because if this variety originates from Japan, then it could have been introduced in 1690 by the Portuguese.
"In 1895, Simon-Louis Frères indicates that this fig tree was brought by a botanist named M. de Sieboldi, during his expedition in Japan to study the flora, between 1823 and 1830."
"In 1845, the Italian Gasparrini names this fig tree 'Hirta del Giappone' (of Japan), because of the small downy fuzz on fruits and leaves, but also because of the oriental origin. "