And here A killed B, which has violated the Criminal Law of People's Republic of China (PRC), that is, a criminal case. The characteristic of criminal cases is that the state investigates the criminal suspect's responsibility, and the victim B cooperates with the public prosecution to investigate the criminal responsibility of the criminal suspect. One party is a citizen and the other party is a judicial organ (organ of state power), so only the criminal suspect can hire a defense lawyer, and the injured party will be prosecuted by the people's procuratorate, that is, the "public prosecution organ and prosecutor" you proposed to the people's court on behalf of the victim, and then the trial will begin.
In short, in the trial stage of a criminal case, the people's procuratorate is the public prosecutor, the suspect is the defendant, the defense lawyer hired by the suspect is his defense lawyer, and the victim cooperates with the people's procuratorate to prosecute the defendant.
If you have any questions, you can also look at the Criminal Procedure Law of People's Republic of China (PRC).
My answer to your question is:
The first suspect, A, was sentenced to death and hired a lawyer or was appointed as a defender by the court.
Second, the victim can't hire a lawyer because he doesn't trust the prosecutor's ability. This is a provision under the jurisdiction of the Criminal Procedure Law, and public prosecution must be initiated by the procuratorate under its jurisdiction. If you are not satisfied with the trial result, the law stipulates the victim's relief channel: 1, and you can appeal to the higher level procuratorate to lodge a protest. 2. You can appeal to file a retrial and start the trial supervision procedure.
In short, these provisions are in the Criminal Procedure Law of People's Republic of China (PRC). This is an established judicial procedure, and judicial work is to act according to law. One of the justifications in criminal procedure is due process, otherwise criminal procedure is an empty law.