Is it a condition for entering Islam that there be an immediate succession between uttering the two Shahadas?

Scholars differ regarding the condition of uninterrupted succession (al-muwālāt) between the two declarations of faith (the Shahadatayn) for one who wishes to embrace Islam. Some consider it a condition, such that the Islam of one who does not immediately utter the second phrase is invalid. Others disagree, not considering uninterrupted succession a condition, and deem valid the Islam of one who delays uttering the second phrase. This is the view the author inclines towards due to the absence of evidence for stipulating uninterrupted succession.