I would suggest that is not the best way to configure this?
If you install as you suggest, you have the
Battery Charger running off the
inverter when there is no hookup, which will do nothing other than waste power.
You could say " I only turn the charger on when I have hookup" which is one way to avoid the problem. However .... with the Auto switchover, you could lose EHU without realising and you inadvertantly have that charger on powered by batteries

The other problem you can get with the same scenario is running the Electric Room heater and the Electric Water Boiler off the
Inverter as well.
Rather then between the EHU inlet and Consumer Unit, I would have the
Inverter coming off one of the Circuits from the CU so you can avoid any risk of the devices you want to only ever work on Hookup (
Battery Charger and Electric Room Heater) being fed by the
Inverter.