The matter is quite complicated. I’ll look into Biography of Hazrat Umer and History written by Tibri… But for the time-being I found this:
Encyclopedia Britanica - The Alexandrian Library had, in fact, been destroyed much earlier, in the fourth century A.D, long before the advent of Islam: "The library survived the disintegration of Alexander’s empire (first century BC) and continued to exist under Roman rule until the third century AD."3 The truth is that one half of this library was burnt by Julius Caesar in 47 BC. In the third century, Alexandria came under the domination of Christians. At another place the same work states that, “The main museum and library were destroyed during the civil war of the third century AD and a subsidiary library was burned by Christians in AD 391.”