Hi,
I was trying to track down some info for you, but I ran into a perplexing problem. The name (both spellings) does not seem to exist in Italy today.
http://www.gens.labo.net/en/cognomi/genera.html
Yet, there are Ellis Island records for both spellings from the town of Mezzojusto. Therefore the name must have existed at one time. The names Sprofero, as well as Sprofeto,( a mistranscription) also appear. Earliest arrival seems to be 1890.
Do you have any US records? (Censuses, draft cards, naturalization details) It might be easier to track these first.
Surprisingly, La Monte is also pretty rare, but also appears on Ellis Island from that town. But, no Giuseppa or Giuseppina.
Where did the family settle when they first got here?
We have a great expert on Italian names on this site, she may be able to shed some light on this.