What is required for the Islam of an original disbeliever who denies religion fundamentally but testifies only to the prophethood of Muhammad?

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Regarding an original disbeliever who denies religion entirely and testifies only, 'Muhammad is the Messenger of Allah,' there are two narrations. One opinion holds that his Islam is judged valid based on the narration where a Jew who testified to the prophethood of Muhammad was prayed over after death, and because affirming the message of Muhammad necessitates affirming the sender and His monotheism, as the Prophet brought the concept of Oneness. The correct opinion, supported by most reports, holds that if the person was a monotheist, such as Jews, his Islam is accepted because affirming the prophethood completes the existing acknowledgment of God's unity. However, if they were not monotheists, such as Christians, Magians, or idolaters, their Islam is not declared valid until they also testify, 'There is no god but Allah,' because denying two things requires affirming both to remove the denial.