score:11
I am sorry this is the only thing I could find.
As a result, we can say with confidence that the library has been destroyed as a whole. For instance, the Tabula Rogeriana, written by the Arabic scholar Muhammad al-Idrisi, ended up in Paris and Oxford, while the book about falconry is conserved in the Vatican.
Among the book that it contained I have found:
None of these survives in original, but we have copies.
Let's see the sources:
Moreover, Frederick's court was an itinerant one, partly because the imperial lands of Germany and northern Italy were traditionally ruled by an itinerant emperor with no single capital or base; partly because the strains of war kept Frederick on the move in Lombardy and central Italy for long periods in the 1230s and 1240s.
After residing in Southern Italy, in the Regnum (and in Apulia in particular):
In 1239-40 Frederick [...] carried with him, it is true, some remarkable animals - an elephant, camels, falcons - as well as his crown jewels and part of his library. Much of this was seized by his Lombard enemies at Parma.
Additional evidence is provided by the fact that:
Art of Hunting with Birds is a thoroughly remarkable piece of science, describing in exact and unadorned detail the nesting habits of falcons and their prey [...] The book survives in two versions [...] but there once existed in Frederick's own possession a very beautiful copy of this or another hunting book. In 1264 or 1265 a citizen of Milan offered Charles of Anjou, count of Anjou and Provence, and soon to be king of Sicily, a copy of the book captured with the emperor's treasures at Parma; [...] This may in fact have been not his falcon book but a second work, on hawks as a whole (of which the falcon is a sub-species). In any case, Manfred searched out Frederick's additional notes deposited in the castles of Apulia before setting to work on his revision of the falcon book, and it seems that Frederick had been accumulating notes and drafts for over thirty years. Sections of the falcon book on the diseases of birds are now lost, and even so the work is a very substantial one; the Vatican manuscript is only 111 folios, but the six-book version reaches 589 folios in a fifteenth-century copy prepared for a later claimant to the throne of Sicily.
Sources:
Frederik II a medieval emperor, Abulafia D., 1988, Oxford University Press
Wikipedia