great where did you buy this ups ?
where did you buy the case?
One important, thing, when your pi is running , and suddenly the main power is cut
normaly the pi go on working on the battery ?
it is diruptive to move from main power to battery ?
The setup I explained above, the RPi is always running off the battery.
The Charger, feels the battery volts. If the battery is at, in this case, 13.8V or more, the charger shuts off charging mode. When charging mode is shut off the RPi is being supplied by the battery. As the charge on the battery drops, the charger, at a set point, starts charging the battery again. This cycle continues.
All those components came from Amazon.
It is not disruptive to move from main power to battery.
Most of the smaller alarm systems just use a small sealed lead acid battery which is supplied with a regulated ( float ) voltage from the mains to keep it charged .
The battery then feeds the alarm - simple and cheap .
Transformer >diode bridge and capacitor > 7805 with zener in ground connection to get 13volts for the battery