Islam, as the last, universal form of the Divine religion, orders its followers to believe in all of the Prophets. Being a Muslim also means being a follower of Jesus and Moses and of all the other Prophets at the same time.
The Qur’an declares:
The Messenger (Muhammad) believes in what has been revealed to him by his Lord, and so do the believers. They all believe in God and His angels, His Scriptures and His Messengers: ‘We make no distinction between any of His Messengers’—and they say: ‘We hear and obey. Grant us Your forgiveness, our Lord; to You is the journeying (2.285)