I have designed my Go Box to include the ability to automatically switch over from the AC/DC power supply to the Battery when commercial power fails, using the Paradan Radio DC Gate 40.
hamsource.com/product-category/dc-power-...ucts/battery-backup/

Here is the issue:
The AC/DC power supply must provide a minimum of 14.2 volts to trickle charge the LiFeSO4 battery.
So, you need to find a AC/DC power supply that will provide that voltage.
Hint:
NOT ALL DO this (usually max @ 13.8v)

I have found 2 manufactures that make AC/DC power supplies that fit the bill. (if you know of other, please post a reply.
Powerwerx sps-30dm
powerwerx.com/variable-power-supply-digital-meters-30amp

MFJ 4230MVP[/b[
www.dxengineering.com/parts/mfj-4230mvp

If you know of others please post a reply.