Welcome to the forum! Pearls are a wonderful thing to inherit and sentimental whether real or faux.
The photos are a bit fuzzy-- it's hard to tell much about the pearls. Can you take closeup photos of a few pearls, including drill holes and the clasp-- the white background you used is good.
Also, are there any markings on the clasp?
Finally, what does the word next to the swan on the box read? It looks like Long or Lang but I can't make it out.
Edit: Must be Lang-- here is another box with the swan and "Lang" that was being sold on eBay:
http://www.ebay.com/itm/ELEGANT-VIN...D&orig_cvip=true&rt=nc&_trksid=p2047675.l2557
Googling I see lots of images of various Lang sterling items but no pearls (
yet, still searching.)