Can a criminal in prison be convicted of murder if already in prison for murder if he kills in the prison?

Yes the person can. The person convicted of the first murder is sentenced to jail time then that murder is done with. If while incarcerated and another murder is occurred then the subject will be go to trial for murder again but not the same person.

You are thinking of double jeopardy. This only occurs after someone is tried and found not guilty. At that point the subject can run outside and say he did it with out being able to be tried again.