Here are the things that don't add up for me:
1. I don't see knots between the pearls. Fine pearl strands usually are knotted between the pearls-- even most imitation pearls are knotted.
2. The pearls are very uniform in color. Cultured pearls, at least the better ones, show some variation in the overtones from one pearl to another in a strand.
3. Silver clasps tend to go with lower end pearls, at least in modern necklaces. Your pearls are so round that they would have to be akoyas (higher end pearls), if they are real. I would have expected them to have a gold clasp.
Edit: My husband just pointed out that it's also unusual to have the word "silver" on a clasp. "925", yes; "silver", no.
However, it's possible that pearls coming from China might have "silver" on them-- but if they come from China, then they are probably freshwater pearls. Again, unless they are high end, they would not be so round.
4. Cultured pearls in a strand fall into a range of sizes, such as 7-7.5mm. Not having been made by a machine, they are not going to all be the exact same size. I don't see that variability in your photos. Matching pearls more closely would make them much more expensive-- in which case, again, they should not have a silver clasp.
I suggest rather than an appraisal, which would be costly, you take them to a jeweler to have a look at them under a loupe. At 10x magnification, real pearls have smooth looking nacre, while imitation pearls look rougher. (Imitation pearls feel smooth but look rough under 10x magnification; real pearls feel rough but look smooth at 10x magnification.)
You may be surprised at who buys imitation pearls. I have lots of them-- I like Majorica, which are very fine imitations-- although I also enjoy my real ones. Jackie Kennedy wore imitation pearls; her famous 3 strand necklace was made by Kenneth Jay Lane. Barbara Bush's pearls were also imitations made by KJL.