I found this from the Hadith about the Prophet Muhammad's letter to Caesar of Rome. D

Rome (Arabic=Rum) in those hadith is not Roman empire that located in place that now known as Italy, but Eastern Rome (also known as Byzantine) that had capital in Constantinople (now Istanbul). And Caesar in those hadith is Heraclius, a Byzantine emperor that lived in Rasulullah (saw) period.

Yes you are right Constantinople was the Eastern Roman Empire.

truthseeker63 said:

Yes you are right Constantinople was the Eastern Roman Empire.

Click to expand...

But later Byzantine left their Roman/Latin culture and civilization and turn into Greek culture and civilization. Even the Byzantine emperor that changed official language from Latin into Greek was Heraclius, in 620 a.d.

And about English translation of hadith that mentioned in links in post #1.
I don't know what is Arabic word that used to call Heraclius in those hadith. But, use "Caesar" to call Heraclius in those English translated hadith is actually wrong. Heraclius was not Caesar but "Augustus" (emperor). Caesar as title was used to call Vice (or assistant of) Augustus.

It could not of been the Western Roman Empire because the Western Roman Empire fell by that time it did not exist.