A fascinating piece of art.
I'm making a few assumptions here. I'm assuming that the signature says Picasso, and the Ermanno was Ermanno Nason. I'm assuming that you're asking if it's possible that this is genuine. It is definitely possible given the information you provide. Ermanno Nason carried out designs for Picasso, amongst others, while he worked at IVR Mazzega, who produced the glass in collaboration with Funcina degli Angeli, in the years 1953-9. There are pictures of a few pieces by Ermanno following designs by Picasso, Cocteau, Leger, and others in Marino Barovier, Venetian Art Glass. The 1940's date doesn't make sense.
Is it genuine? I wouldn't even hazard a guess. I think you'd need to find a very reputable dealer who is used to dealing with very high end pieces of glass in order to answer that question. Dr. Fischer in Germany, Rosella Junck in Venice, and Dan Ripley in the States spring to mind, although others on the board I'm sure could suggest more. Generally, the glass shown on this board won't have a value in the thousands. This would, if it's genuine.
I'd love to hear what you find out about the piece.