This is the 23rd most frequent Ukrainian word.
після
"Після" means "after" in English.
In this sentence, 'після' denotes a sequence in time, indicating that the event 'going home' occurred following 'lunch'.
Ми пішли додому після обіду.
We went home after lunch.
Here, 'після' is used to indicate an event (feeling inspired) that follows another event (reading the book) as a temporal sequence.
Після прочитання книги я відчув натхнення.
After reading the book, I felt inspired.
In this context, 'після' situates the moment of hearing the news relative to the previous event of receiving a friend's call.