Bismillahi Al-Rahmani Al-Rahim
Could you add a couple of lines on the cases:
In the previous message I wrote that
[b]oth Zad al-mustaqni` (section c2.2 in the lessons) and Nail al-ma'arib (1.122) say that a prayer is considered a current performance provided that the inaugural takbir [takbir al-ihram] occurs within the appointed time - even if the adhan is made within moments after that takbir.
And contrasted it to the Shafi`i position with saying that
[t]his differs with the Shafi`i madhhab where current performance is "performing an act of worship or a rak`ah during its [appointed] time" (Zakariyah al-Ansari, Ghayat al-wusul. p16. cf Taj al-Din ibn Al-Subki, Jam` al-jawami`, 1.106).
So, case #1 where one complete rak`ah is prayed within the prayer's time and the remaining after it: the prayer is a current performance according to both the Hanbali (since the inaugural takbir occurred within the appointed time) and Shafi'is (since at least one complete rak`ah has been performed within the appointed time - for the respective madhhabs).
As for case #2 where less than one rak`ah is prayed within the prayer's time and the remaining after it: the entire prayer is current performance according to the Hanbalis (since the inaugural takbir occurred within the prayer's appointed time), but is a make-up performed according to the Shafi`is (since less than one complete rak`ah occurred within the appointed time).
And Allah knows best.
Wa al-salamu `alaykum,