Hence when A says
"B is a lying monkey. I am human."
Both the statements are lies.
And when B says "A is telling the truth."
The statement is again a lie
A cannot be truthful because if he is , then B's statement would be a contradiction. If he is not truthful, his second statement would also be a lie. Hence he is not human either. Hence he is a lying monkey.
B cannot be truthful either as he says that A is truthful which A is not. He can only be a lying monkey or a lying human.
Since A's statement "B is a Lying monkey" is a lie... B can only be a lying human