What I think happened here is a case of gradual exaggeration. Benito Mussolini, who started the Italian Fascist party, was a socialist. But he got kicked out of the socialist party for supporting Italian involvement in WWI.
Since he was no longer in the socialist party, he started his own organization, which eventually became the fascist party. Although the opinions of the fascists and the socialists differed in several respects, most of the fascist ideology was simply socialism. Therefore the opinions of the fascists and the socialists was quite similar in many respects.
A similar thing happened in Germany, where DAP, the German Workers Party, acquired some nationalist opinions and finally turned into NSDAP, the Nazi party.
The discourse, propaganda, opinions and target interest groups of the socialists and the Italian fascists and German nazis was very similar, although the socialists emphasized class while the Italian fascists and German nazis emphasized the nation. The politics they proposed was also very similar.
But by the time Mussolini actually formed the Fascist party, it was seven years since he was kicked out out the socialist party, and there was no reason for him to just take the socialist party's program and change it a bit. I also can find no support for this claim, and I think that would be more widely known if it was the case.
So, no, they did not share the same electoral programme as far as I can figure out. I did find the 1920 program of PSI, and the 1921 program of PNF, and they are not the same at all. But that doesn't prove anything, you would have to compare the program of PSI for all it's years with the programs of the several socialist parties in Italy during all their years, and to do that you probably need to go to Italy. :-)