Maybe the question here should be does the Christain version of events fit the rest? the answer is no, Jesus was a pratacing Jew and did not make much changed to the sacred law. christatans believe that God is three then why is none of the Prophets claimed this, surely if they where prophets shouldn't they know? Why is it tht the trinty wasnt paret of christan theology until the roman emepore costintine forced it upon the people? Why is that many pagan symbols where adopted into Chrstaintiy, they used to worship on a saturday then changed it to sunday, the day of the sun. The pagan deity called Baal was believed to be born on the 25th, he was the son of the sun.
Also in the persian mythriac religion the son of god was sent to cleanse the world of sin, this what the bible says. Why is that that Jesus didn not change the religion as much as others did yet he has the right to do so.
Its christanity that doesnt agree with Jesus (upon him eace) not the other way round.
As for Islam, and Muhammad (peace and blessing be upon him), the Hajj rights are from Abraham (upon him peace), the sacrficie etc, the fasting from David and every Prophet, the charity from every Prophet.
The daily prayers: The first to pray Fajr was Adam upon him peace after he was taken out of heaven into the darkness of the world, in the middle of the night, he was overtaken by extreme fear. When dawn came and the light began to appear, he prayed to Allah ta’ala out of gratitude.
The first one to pray Zuhur was Ibrahim when it was called out, “O’ Ibrahim you vision is true,” this was at the time of Zawaal.
The first one to pray Asr was Yunis when Allah freed him from the belly of the whale and the prayer was in the time of Asr.
The first one to pray Magrib was Isa upon him peace, when Gibril informed him that his nation would call him one of a trinity then he prayed three units and this was after sunset.
The first one to pray Isha was Musa upon him peace when he arrived on a path that left Madiyan, he had four problems and he prayed four units.
The first one to pray Witr was the Messenger of Allah peace and blessings be upon him on the night of accession in the station of Gibril at the lote tree.
Islam is the old religion and Christanity is the new one.