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Without holding it in hand, it's difficult to determine what kind of stone it really is. In France in the early 20s (era of your necklace), Chrysophrase was popular, comes in several colors green being most common, Jadeite and jade of course, and even plain glass blown very artistically into beads. Weight and hardness (on Moh Scale) can help determine exactly what you have. (Difficult to weigh a bead without removing it from the necklace, however.)
It'd be nice to identify it properly but if you can't the piece should stand on its own merit, an interesting 1920s era design necklace!