Asalamulalaikum. Does praying a salat right after the locally calculated time for Azan be considered as being in the duration of waqt e Fazilat, or do I have to calculate the timings from one salat to another? JazakAllah.
You don't need to calculate the timings on an individual level. The Adhan itself is an indication of the time for prayer and thus you can pray immediately i.e. Waqt-e-Fazilat.