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.