How to detect completion of Lithium-Ion charging
Charging is usually terminated based on a charging profile and some termination current.  So if the charging voltage is say 4.35V, the cell will charge at a current based on the state of discharge.  When the current drops below a threshold, charging is terminated.  Termination current and charge voltage are often programmable in a given charging system.

Here's an example from the TI bq25895 single cell charger: