Here's the thing... our grandmothers also bought costume jewelry. Many times this was all they could afford, since cultured pearls were very expensive then-- and a long strand like yours with all the pearls the same size, if real, would have been really expensive. It would take a long time to match so many pearls. That's why many older strands of real cultured pearls are graduated in size; it kept the cost down.
Sometimes our mothers and grandmothers thought their jewels were real when they were not. My MIL had a strand of pearls given to her by my FIL; she, and he, and the rest of the family all thought they were real. After her death I examined them and guess what? Imitation. That didn't mean they weren't precious to her. Her husband gave them to her, and that made them precious.
I will recommend to you a fairly simple test. Wipe the pearls clean with a soft damp cloth. Then gently rub one against another. Real nacre will feel a bit resistant; imitation pearl coating will slide fairly easily without resistance.
Look at the drill holes. Sometimes peeling of imitation pearl coating occurs around drill holes, revealing the glass bead underneath. If the holes are beveled, that is indicative of imitation pearls (although many imitations are not beveled.) If there are swirls of extra coating near the drill hole, this too is indicative of imitation pearls.
All but the cheapest imitation pearls have glass beads inside, so you can't judge by their weight.
If you find them a bit resistant with the rubbing test and don't see anything near the drill holes to lead you to believe they are imitations, then take some more photos-- in focus-- against a white background is best (like a paper towel), without flash. Include some closeups using your macro setting (the little flower icon.) Take closeups of any surface flaws you see. Some are typical of real pearls. Photograph any marks or stamps on the clasp indicating the kind/karat of metal or manufacturer.