Green agate or moss agate. Or jade.
They are not transparent at all. They might be jade. Fairly thin stones. I didn't think jade was that dark.
Jade can come in many colors.
I have a piece of New Zealand Jade.
I have been told it is the hardest jade in the world.
Here is a link to a site to help you to identify.
(Caution with point 4! )
If it is not jade, what would you think it is?
Nephrite, emerald, verdite, agate.
As most of the stones for your grandfathers legacy are agates, I'm thinking the latter.
But it does not have the shine as an agate.
Have you tried identifying it with the link?
Jade, no facets or crystal formation smooth, I'd say jade.