Does the "electricity saving box" work?
Power factor correction uses capacitors to add leading reactive power (VARs or kVARs for large loads) to counter lagging reactive power required by inductive loads like fluorescent lights or motors.
Reactive power goes back and forth between source and load.  The capacitors act as a form of battery decreasing reactive power supplied by source.
It does not change the real power W or kW.  You pay for energy in kWh.  Energy = P t
So power factor correction will benefit the power company, but have no impact on your power bill.  Actually, the powers involved are meaningless for homes.
Claims are not reality.
Large consumers require power factor correction if pf is &lt; 0.9, because they pay for kW in kWh, but power companies must provide kVA.  Best pf = 1.  Companies with a poor pf must pay a surcharge for kWh used.

GreatScott! debunks this. Chinese Power Saver - Does it actually save power?  He even mentions claims.
Essentially the device connects a high voltage 2μF capacitor across the mains terminals.  Rest of the parts discharge capacitor when disconnected from circuit