Its hard to say how much annual savings she will get.
It depends on how much hot water she and the rest of the family use. If she lives on her own and has short showers then the cost of heating water might be low, so the savings will be low.
However, it might be worth it for convenience and living comfort.
Exactly what is she getting for the money. Is this connecting it to the current gas boiler and adding zones. Will they be putting a timer on and the ability to switch on the hot water by texting the controller. These features are very handy and can save money by allowing you to control the amount of hot water you heat.
If the immersion tank is not working, she needs to fix it, so its worth fixing it with improvements.