Islamic sources mention Muhammad sending letters to various Heads of States and so I want to know if there is any evidence of this from Byzantium's records?
If it's evidence from Byzantine sources you're after then the answer is no. If you're interested in seeing what Byzantine sources do have to say, then the best source to consult is Robert Hoyland's Seeing Islam as Others Saw It, which provides a large number of non-Islamic sources on early Islam in English translation with Hoyland's own commentary.
In regards to the question of whether there is any historical evidence at all, well there is quite obviously the Arab sources that suggest there was communication. There is debate about whether Muhammad's letters to Heraclius are legitimate, but Heraclius' alleged replies are unanimously rejected. For more on that see "Muhammad and Heraclius: A Study in Legitimacy".
Sources
El-Cheikh, Nadia Maria. "Muḥammad and Heraclius: A Study in Legitimacy." Studia Islamica, no. 89 (1999): 5-21. doi:10.2307/1596083.
Hoyland, Robert G. Seeing Islam as others saw it: a survey and evaluation of Christian, Jewish and Zoroastrian writings on early Islam. Princeton, NJ: Darwin Press, 2007.