Thank you for the additional photos. Assuming these are akoyas, the strand seems to be well matched for color, and round, which are more valuable than baroque. Somewhat difficult to tell about the luster of the pearls, but probably not AAA quality. Unable to assess the nacre thickness from a photo. Vintage akoya pearls often have thicker nacre than newer pearls, but with this strand being only 5 years old, we have to assume they have average nacre thickness.
I asked about the clasp because I thought it might be a "temporary" clasp, allowing the customer to try a strand to check for length and see if the color was flattering, and would account for the necklace not being knotted. I still can't tell for sure, the clasp may be a traditional fish hook.
I checked what several of our respected forum members offer in a 16 inch AA+ 7.5-8mm akoya necklace, knotted, with 14k gold clasp, and found necklaces for just under $1000 and earrings under $200. So that would be the approximate retail replacement value, for insurance purposes. However, if you were to sell (on ebay), you would probably receive only 15-20% at most.
I'd recommend restringing the pearls, having them knotted in between to prevent the pearls from wearing on each other and make the necklace more flexible, and perhaps add a 14k gold clasp, especially if this one is difficult to open and close.
I hope your wife will wear and enjoy her lovely pearls.