Maybe you can specify what the carta di sanjorno is for? I am German, but I don't know the Italian asylum system or the cards they use. Does this probably have to do with the "permesso di soggiorno"?
If your first step on European ground was in Italy and if you were granted asylum there, I suppose you will not be allowed to leave the country without losing the refugee status and you will not be granted asylum in Germany.
If you want to move to Germany to work, you will find all laws and regulations on the webpage of the German ministry for migration and refugees (BAMF - Bundesministerium fuer Migration und Fluechtlinge):
In every case, it will be better if you inform yourself very well about your possibilities BEFORE you move to Germany. Keep in mind that even if you have a residence permit in Italy, this is not a naturalization, so you will be not considered European in Germany, but a "non-EU citizen"/"citizen of third countries"