Umayr bin Ishaq (may Allah have mercy on him) says that the Messenger of Allah (peace and blessings be upon him) wrote to Kisra and Caesar. Caesar kept the letter respectfully, whereas Kisra tore it up. The Messenger of Allah (peace and blessings be upon him) said: "As for these (the people of Kisra), they will be torn to pieces, and as for those (the people of Caesar), they will have a remnant."
Imam al-Shafi'i (may Allah have mercy on him) said: The Messenger of Allah (peace and blessings be upon him) gave the people the good news of the conquest of Persia and Syria.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب السير / 18608