It is very easy to knock up a simple UPS to power a modem, all you need is a crimping tool and some connectors and some wire, and a lead to connect to the router. Anyone used to working around computers could do it.
Connect SLA batteries in parallel, get a proprietary smart charger. connect up...done. I also added a diode in the supply to the router to drop the voltage a tad, but not absolutely necessary. The second photo shows the charger, the grey thing with an orange light showing.
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