Earlier quoted context omitted.
That's an oversimplification - menopause results from decreased levels of hormones that would normally be secreted during the process of egg maturation, among other potential causes [see ref 1]. Further, all the eggs a woman will ever have are created while she is developing in her own mother. This is totally distinct from stem cells, many of which are able to generate new stem cells throughout our lives, albeit at a…
http://www.webmd.com/infertility-and-reproduction/news/20040...
While the principal author of that article published an equally-controversial paper in 2005, follow-up studies suggest that there are no newly-generated egg cells in mammals [1]. I think it's fair to say, again, that stem cells don't play a role in maturation of adult egg cells.