Is the prayer of an unbeliever sufficient to establish his conversion to Islam?

Primary text

The prayer of an unbeliever establishes his Islam, regardless of whether he performed it in the Abode of War (Dar al-Harb) or the Abode of Islam, whether in congregation or individually. This applies whether the person is an original unbeliever or an apostate. The evidence is that the prayer is a fundamental pillar exclusive to Islam, functioning like the declaration of faith (Shahadatayn) to establish Islam. The established proof for the others is that whatever action establishes Islam in the Abode of War must establish it in the Abode of Islam, such as the Shahadatayn. The possibility of hypocrisy or Taqiyyah (dissimulation) is negated by the very performance of the prayer, just as it is negated by the Shahadatayn.