Does an apostate whose apostasy is proven become reconciled to Islam solely by testifying to the Shahada (testimony of faith)?

Primary text

If an apostate's apostasy is established by evidence or other means, and he subsequently testifies, 'There is no god but Allah, and Muhammad is the Messenger of Allah,' his reconciliation is accepted, and he is set free without being forced to confess to the act of apostasy. This is based on the Prophet's command to fight people until they say the testimony of faith, by which their lives and properties are protected, except by due right, and their reckoning belongs to Allah. This principle is applied because the testimony of faith establishes the Islam of the original disbeliever, and similarly, it establishes the Islam of the apostate. There is no need to investigate the validity of the prior apostasy once Islam is established.