There are a couple of ways that she can do this. One is to find a website that provides information about the kind of jewelry that she makes and add a page of her own with her stuff; Another is to create a website and start marketing her stuff as a business of her own; Another is to start selling her stuff on some auction type sites and see if it sells or what sells best. To find out if there is a real market before making that kind of investment though she may want to start out selling locally at craft fairs and at some of the local boutiques. Then she can get a feel for what stuff sells best and how much to charge. Selling online will cost her an investment that she might avoid if she starts out locally first.
Etsy.com is the website that I was going to recommend. I would think once you get your Etsy website up and running, you d have your own web address and then could use it easily give people access to view the jewelry your mother makes.
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Another place to look at would be Ruby Lanehttp://www.rubylane.comSarit.http://sarit-jewelry.com
Etsy is an excellent place to start.