Oh my America. Kathleen, you will need to get the pearls x-rayed to certify that the pearls are indeed Natural pearls rarest of rare natural jewels of the sea. To find a rare Natural pearl is finding manna in the wilderness.
Provenance, (which you are able to provide) refers to the chronology of the ownership or location of an historical object. This information, is extremely important in terms of premier jewelry and pearls which usually only change hands privately, and being that the pearls are rare, possibly natural pearls and over 300 years of age!
I hope you have these pearls stored separately away from harder gems. GIA in the US have the facilities to X-ray pearls.