Does the time difference between Cairo and São Paulo change during the year?

Yes. Because of daylight saving time the gap moves between +5h and +6h.

When is the best time to call São Paulo from Cairo?

Between 15:00 and 17:00 in Cairo, which is 09:00 to 11:00 in São Paulo.

Cairo is 6h ahead of São Paulo. This gap is not fixed: daylight saving time moves it between +5h and +6h during the year.

Cairo

Egypt

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São Paulo

Brazil

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A 9-to-5 day in each city overlaps for 2h. That is 15:00–17:00 in Cairo, which is 09:00–11:00 in São Paulo.

City	Time zone	UTC offset
Cairo · Egypt	Africa/Cairo	UTC+3
São Paulo · Brazil	America/Sao_Paulo	UTC−3

What is the time difference between Cairo and São Paulo?: Cairo is 6h ahead of São Paulo. This gap is not fixed: daylight saving time moves it between +5h and +6h during the year.
Does the time difference between Cairo and São Paulo change during the year?: Yes. Because of daylight saving time the gap moves between +5h and +6h.
When is the best time to call São Paulo from Cairo?: Between 15:00 and 17:00 in Cairo, which is 09:00 to 11:00 in São Paulo.