To what extent is the hadith that speaks of the conquest of Constantinople and Rome authentic?

Ahmad and Al-Hakim narrated, and Al-Albani authenticated, that Abdullah ibn Amr ibn al-Aas reported that the Prophet (peace be upon him) was asked which of the two cities would be conquered first, Constantinople or Rome. He replied, "The city of Heraclius will be conquered first," referring to Constantinople. Constantinople was indeed conquered through battle by Sultan Mehmed the Conqueror, but its conquest without fighting has not yet occurred. Sheikh Ahmad Shakir mentioned that the conquest promised in the hadith (definition) will happen when Muslims return to their religion, and that the conquest by the Turks was a prelude to the greater conquest. The Islamic conquest of it will return at the end of time, as Muslim narrated from Abu Hurayrah that the Prophet (peace be upon him) said it would be conquered by the Muslims' saying of 'Allahu Akbar' and 'Subhan Allah', not by weapons, and this will be before the emergence of the Dajjal.