Beijing is 5 hours ahead of Cairo
Best overlap: 8:00 AM to 1:00 PM in Cairo is 1:00 PM to 6:00 PM in Beijing.
Both offices are open during 8:00 AM to 1:00 PM Cairo time, which is 1:00 PM to 6:00 PM in Beijing. You've got a decent 5-hour window. Set a recurring time near 8:00 AM in Cairo (1:00 PM in Beijing) and stick to it. Watch the DST gap — when Cairo changes its clocks and Beijing stays the same, this window slides by an hour.