Hallo, Oh No, hold ON what is your urgency? Even by reading your message you seemed confused and in a rush. Take a deep breath, relax and be calm.
Moving to Germany needs a gigantic patience. You had Greece documents and that was a good move but seeking Asylum in Germany was a big mistake. Now that the authorities has answered and said you have to wait. Chances are you will be deported back to Greece.
And if you move to Italy (YES) the authorities there will know ACTUALLY they already know your process in EU countries hence that is why its called called EU,they share this information the time you apply visa or seek asylum through fingerprint.