Charge batteries from a charger not the inverter? (UK)

I have a 4kw array with a SolarSofar inverter which charges the 12kw battery at a max of 3kwh. It is a standard 48v battery which can be daisy chained. I am looking to buy another battery for the winter but do not want to have to buy another inverter to charge it. At the moment I have 4 hours cheap electric in the early hours of the morning and it will not be able to charge both on its own.

Is there a way I can charge the batteries via another source but still have them connected to the inverter?

I would ideally like to set the charge times as well as the inverter does not have remote access for the those settings. Maybe via a smart plug? My house is on a Home Assistant setup so would be using that to charge the batteries as the cheapest times. This is not necessary but would be liked.

Thanks all.