The Sunni and Shia split because after the death of Muhammed, Muslims couldn't agree on who should lead Islam - the Sunni branch accepted Abu Bakr because he was agreed to be the best candidate to be caliph. Shia, however, believe the caliphate should be descended through Muhammed's family.
Sunnis believed that after Prophet Mohammed (PBUH) died that his friend and companion Abu Bakr was the new Caliph (Leader of Muslims)
Shia believe that Ali (Prophet Mohammed (PBIH) Cousin, Son-In-Law, and close companion) was to be the next Caliph.
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