I have no idea if a Note 3 battery will work in a Note 2 but if you need to get her a new one why not just buy one that's made for a Note 2? The Note 3 uses a 3200mAh battery while the Note 2 uses a 3100mAh battery but that's a negligible bump up in capacity so even if dimensional-wise the two are the same I'd just stick with a Note 2 battery replacement. If it were a matter where she had a spare Note 2 to supplement her daily usage phone than it might be worth experimenting. Just my opinion of course.