Hi Jaime
It would be interesting to find a bit more about this cultivar.
Badalhouce was up to the 16th century , also the Portuguese name of the Spanish town known today as Badajoz the capital of the Estremadura Province.
A Spanish white fig (two crop) from the Province of Andaluzia, known by 'Pezonuda' bears a name close to the Badalhouce synonym - Paçanudo-
May be through your good contacts in Spain we get a bit more light into the true origins/names of this variety which one good day landed in the Pico Island in the Açores Arquipelago
Francisco