It can't stack because it requires attunement. You can only be attuned to three items at a time, and you cannot be attuned to more than one copy of an item.
https://www.dndbeyond.com/sources/basic-rules/magic-items

If a dm asks for a check. Lets just say for argument intelligence CHECK not an ability that uses intelligence just a check, do this add plus 1?

Quote from Neoskull >>

If a dm asks for a check. Lets just say for argument intelligence CHECK not an ability that uses intelligence just a check, do this add plus 1?

 An "Intelligence check" is just short for an "Intelligence ability check" so you should add the +1, even if no skill proficiency is being used.

Quote from CaenixDrae >>

It can't stack because it requires attunement. You can only be attuned to three items at a time, and you cannot be attuned to more than one copy of an item.
https://www.dndbeyond.com/sources/basic-rules/magic-items

It stacks with items like a ring or cloak of protection, or any other items that give bonuses to abilities and saving throws

Still wonder if I could argue that this stone also works in Moon Druids Wild Shape, since my items "merges into my new form" and is technically still with me ^^
Alternatively I might have to try fashioning some kind of necklace that would be practical enough to wear with at least some of my forms.

Nice to see this didn't get the nerf hammer.