S1: The matter was resolved amicably between the group even though there were so many of them. S2: Among them the two never have problems sharing what they have.

The traditional rule is that 'between' is used when referring to two distinct entities, and 'among' is used for three or more. In S1, the matter was resolved within a large group ('so many of them'), so 'among' should have been used instead of 'between'. In S2, the reference is to 'the two', which involves only two people, so 'between' should have been used instead of 'among'. Both sentences misuse the words, so both S1 and S2 are wrong.