Solar energy stored in battery can be utilised when AC mains is absent (in inverter mode) thus the solar energy will be stored in the battery and can be utilised when AC mains gets cutoff

As long as the mains is present solar power is kept stored; in case of PCU, solar charging of battery takes priority during solar day

Battery charges through solar until it reaches full charge voltage (typically 14.2V); after battery is fully charged, the load is fed via battery in inverter mode thus AC power is not used in presence of solar power,

After the battery gets fully discharged (up to say 11V), the mains takes over charging as well as the load is fed through mains only.