Lost soggiorno/ denuncia di smarrimento obtained/travelling soon

Hello Members, I am from the Philippines and has been here in Rome for 2 years now as a student. I have applied for the renewal of P.di.Soggiorno already and already made the fingerprint. The problem is early this week I lost my still-valid P.di Soggiorno. I already obtained from the Questura/commissariato a "verbale di denuncia di smarrimento". So apart from the receipt from the Poste, I just have this 'Verbale' (a one page document certifying that I lost my PdS). I am travelling next week to the US and going back on August 11. But come August 21, I am going to Schengen countries. Is this 'Verbale' enough to be presented for going to Schengen countries and for coming back to Italy? Kindly, I would appreciate your knowledge on the matter.