Say a person X appeared as a witness in a case where the judge was presiding in a criminal case (Jugendstrafsache). The testimony of X was welcomed and appreciated highly by the prosecutor as well as the judge.

X is not an EU citizen. X wants German citizenship under "special integration" circumstances. Can X request the judge to write/sign a draft letter that states that X has acted in a manner as would be expected of a German citizen?

Broader question: Are people allowed to write to the judiciary for any such relevant requests at all?