Be careful, not all Li-Ion batteries have built in protection.
The ones that do include it have it as more an emergency measure that intended for normal use and the cut-off voltage really should be slightly above the proper full charge voltage.
Also, that does not provide any current limiting.
If you look at the voltage vs charge state graph for a lithium cell, the they charge at a constant current until they reach full voltage.
The current then starts to drop well before full charge, possibly not much above 50%
The charger needs to keep its connection to the cell or battery until the charge current has dropped to a low level for the cells to really charge properly.
If the cell voltage protection triggers, the current drops instantly to zero and there is no full charge.
I have a couple of lamps where the designer seemed to think only a battery protection board was needed, using a USB connection for charging.
They both blew the charge boards the first time I connected them to a USB power unit, as the charge current was unrestricted and was too much for the protection IC.
I added charge controllers & new protection boards inside them to get them working again.