As-salamu `Alaykum warahmatullah wabarakatuh (May Allah's Peace, Mercy, and Blessings be upon you!).
I would like an explanation of the following:
How do we calculate the last portion of the night? Should we calculate the time starting from the Maghrib (Sunset) Salah to Fajr (Dawn) Salah or starting from `Isha' (Night) Salah to Fajr (Dawn) Salah?
All praise be to Allah and peace be upon His Messenger, upon his family, his Companions, and those who follow him.
The night begins with sunset and ends with dawn, so if the sun sets at five O'Clock PM and the dawn starts at five AM, then one-third of the night equals 4 hours and two-thirds are 8 hours, hence the last third of the night begins at one AM to five AM (and ends with the Adhan (the call for Salah) of Fajr.
By this way, we can calculate the half, the third, and the two-thirds of the night. So, the first third of the night starts at nine, half of the night starts at eleven, and the last third starts at one AM to five AM, which is the time of Dawn.