Can a lawyer communicate with the competent prosecutor and make suggestions on sentencing?

In this regard, the law does not prohibit.

Article link: Article 170 of the Criminal Procedure Law?

When examining a case, the people's procuratorate shall interrogate the criminal suspect, listen to the opinions of the defender, the victim and his agent ad litem, and put them on record. If defenders, victims and their agents ad litem put forward written opinions, they shall attach a volume.