Unfortunately no; first the court won't accept papers from a third party; rather one of the parties need to submit it to the court as an attachment to a legal filing (ie motion, stipulation, petition etc).
Since the court cannot appear to favor one side over another, anything that is presented to the judge will be served on the other party- as each party has a right to cross examine witnesses, examine evidence so they can challenge its validity, etc.
If one mailed the letter to the judge, the clerk would dispose of it and not present it to the judge.
Under the Judicial Code of Conduct, a judge could be disbarred if they allowed for ex parte (one sided) communication.
So if the party wishes to have the statement considered, it would need to be submitted to the court and sent to the other party.
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