Hi char,
How nice to inherit pearls, especially with such a pretty clasp! Given the clasp and that they seem to pass the tooth test, I expect they are genuine pearls. However, clasps can be changed when pearls are restrung. So let's look at a few other factors.
Shape: Are they 100% round? They seem a bit flattened but that may be camera distortion. If they are fully round they are either akoyas or imitations.
Surface: The surface seems quite clean. This can be true of better akoyas or imitations. Please take a close up of any blemishes you see. In particular check out the center pearl, #24 from the clasp.
Edit: I just saw your second post with the new photo. A three strand clasp was adapted to be strung onto this strand.
The surface in the new photo makes me think they are akoyas but do post photos of any flaws you see and answer whether they are really all round. FWP tend to be a bit off round.