AIO charging efficiency and Electric Vehicle

I have a 13.5kWh AIO with 6kW inverter.
(a) If I charge AIO as a stand alone I get about 36% SOC per hour.
(b) If I charge AIO whilst EV is charging this reduces to about 24% SOC per hour.
(c) If the AIO is charged after the car this can be between 22-27% SOC ph.
The Grid Power reported for b/c seems to be lower but why I do not know especially after the car has finished. Charging battery first then car seems a solution. It would be good to resolve as the overall grid consumption for the battery charging appears similar but the SOC is definitly lower in b/c combined charging so clearly not as cost effective. Any thought appreciated. Mole.

mole Could you please provide battery charge graph, from times when you both charged and did not charged EV?
I decreased charge speed to about 2.5kW, because I have 6 hours to charge it to full. You want to charge battery so quick, I assume you must be on Octopus Agile or something, and have much less time do to so cheaply?