As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.
My initial reaction was that the J. Genitori was the deceased person's name with Genitori being a surname. I thought the P.P. below it could be the an abbreviation of the Latin words Patri Patriae-which was a title.
Wouldn't "rest in peace" be abbreviated in Italian as in English as R.I.P. for "riposi in pace?"