I think this question would be better if the second inhabitant said “He says he is a Knight.” Then later said “He is a knight and so am I,” to make it clear they are two separate statements that both must be truthful/lies, instead of the possibility mentioned above in other posts, where his statement is half lying.

1 is either a Knight or a Knave.
Assuming he said “Knight”, then
2 is TRUE and 3 is FALSE
OR
2 is FALSE and 3 is TRUE
so
Knave, Knave, Knight or
Knight, Knight, Knave
are both possible solutions.

It was never specified what the original said. He could have said ‘I am a native’ or ‘I don’t know’ or some such other trivial thing, and the second guy could very well have lied about it while still stating thusly. From that perspective, both possible solutions (Knave, Knave, Knight and Knight Knight Knave) are correct.

@why and hahaha: that is not actually true.
We know that #1 said “I am a Knight”. Whether he were a knight or a knave, he could not have said “I am a Knave”, because that would either be lying from an honest man or honesty from a liar.

Since that is true, and #2 reported it as such, then #2 must be a knight and so must #1.

knave, knave, knight is another possible solution

Wrong. The third guy never said what the first guy actually said. He just says what the first guy actually is, and what he actually is. That would mean the first guy lied and said he was a knight when he was actually a nave like the third guy said. The second guy would have lied about himself, and the first guy making him a nave.

So it works as Knight,Knight,Nave as well as Nave,Nave,Knight.