Age spots are nothing but sun spots. They are caused by being out in the sun, on sun-exposed skin areas, usually, areas not protected with sunscreen (on the forehead and the back of the hands and arms)
Your mum, needs to apply good-quality sunscreen of at least SPF 15 to keep them from darkening and will help prevent new ones.
The juice of a fresh lemon rubbed on with a cotton ball twice daily where the age spots are, in six to eight weeks, will cause to begin to fade away.
Rubbing a piece of sliced red onion has the same effect like lemon juice since has the same peeling acid as fresh lemon juice.
These spots are harmless, but if your mum notice an increase in size or "bizarre" color changes, she'll need to see her doctor immediately.

Good luck with the home remedies!
Marija