Provided the inverter is in good working order, buy it. According to the specs the charge voltage is adjustable so the 14.4V isn't an issue.
Inverter OFF 60 ma 60 ma
Inverter ON in Load Demand Mode 160 ma 160 ma
Inverter ON - Load Demand OFF 1.8 amps
It draws 60mils OFF and 160mils in standby, that's not bad.
I would definitely test it before you give her any money. I can't imagine anyone "forgetting" to take it with them, unless they didn't know what it was.