short_bob,
Since the perfume belonged to her mother, it may be a vintage formulation of a perfume that has since been discontinued or reformulated. (Many of these can still be found on eBay.) Do you have any idea when she bought it? How old was your mother in law? Did she buy "nicer" clothing, shoes, bags or was she more budget-minded? If she splurged a bit on accessories she may have on perfumes as well.
There are some folks on here who are very good at blind sniffs-- figuring out what a perfume is from smelling it. You could swab some of the remaining perfume from the broken bottle carefully with a clean swap, seal the swab in a ziplock bag and mail it to one of these excellent sniffers who may give you an idea of what it is. I won't volunteer for this, I'm not so good at that, but someone else here may.
You could also take it to a perfume counter, preferably at a store like Saks or Neiman Marcus, and sniff fine perfumes, trying to identify it that way. Visit Guerlain and Chanel counters and ask the sales associate to sniff the swab too. But it may be difficult to do this if the perfume has changed over time, and it may have done so if it is quite old.
Still, it would make for an interesting project for us here-- smell the swab and identify the perfume.
You might want to surprise your wife with the bottle but then enlist her cooperation in the scent identification project. Did your wife wear the scent at all? Can she compare it to any other perfume she has smelled? Flowery, sweet, powdery, spicy, any descriptors would help.