Babur, the first Mughal emperor, was succeeded to the Mughal throne by his son, Humayun. Option 1, Sher Shah, is incorrect as Sher Shah was a rival of Humayun and briefly overthrew him before Humayun regained power. Option 2, Akbar, is incorrect as Akbar was Humayun`s son and he succeeded Humayun to become the third Mughal emperor. Option 4, Bahadur Shah, is incorrect as Bahadur Shah was the last Mughal emperor and he ruled much later. So, the correct answer is option 3, Humayun, who succeeded Babur as the second Mughal emperor.