It really depends on which inverter you are referring to.
In general, for a 12V lead-acid battery, charging voltage is between 13.5V and 15V, depending on required charging current.
For a multistage charger, the bulk stage uses a voltage between 14.5V and 15V.
During the trickle stage, it uses a voltage between 13.5V and 14V.
There might be more stages, eg absorption, but this depends on your inverter.
If charging is terminated, it's done either when the battery voltage reaches a certain level (13.5V - 14.4V, depending on charging and sensing method), or when battery charging current falls below a certain level. Again, we don't know if the inverter terminates charging or employs trickle charging.
Hope this helps.
Tahmid.