alternating power source for Sure 2x25W TPA3123 amplifier board

Greetings everybody!
I have some knowledge about systems from when I used to install car audio stuff. I came across a nice box I want to build into a home/outdoors boombox.
Sure 2x25W @ 4 Ohm TPA3123 Class-D Audio Amplifier Board will feed 3-way system with small sub on one channel and set of 3 inch components (everything is 4 Ohm) via passive crossovers.
AC Power supply: Sure 24 VDC 6A 145W Regulated Switching Power Supply
Board has two power inputs, but only one can be used at the time.

Question: how do I connect battery so I can switch between power sources and have battery charge while plugged into AC?
I plan to use small sealed 12V battery (battery recommendations are welcome, as well).

I tried PE tech support, but they couldn't help

Thank you in advance,
Aleksey