public interface IOutputMessage
  {
    void OutputMessage(string message);
  }

  internal class TTMyTextWriter : TextWriter
  {
    private readonly IOutputMessage outputMessageDevice;
    public TTMyTextWriter(IOutputMessage OutputMessageDevice)
    {
      outputMessageDevice = OutputMessageDevice;
    }

    public override Encoding Encoding => Encoding.UTF8;

    internal void OutputMessage(string message)
    {
      outputMessageDevice.OutputMessage(message);
      //base.WriteLine(message); // <--- No, no, no need to do that !
    }

    public override void WriteLine(string value) => OutputMessage(value);

    public override void Write(string value) => OutputMessage(value);

  }

....
    private delegate void DelegateOutputMessage(string message);

    internal TTMyTextWriter MyTextWriter = null;
....
    public void OutputMessage(string message)
    {
      InnerOutputMessage(message);
    }

    private void InnerOutputMessage(string message)
    {
      if (TxtMessage.InvokeRequired)
      {
        DelegateOutputMessage d = new DelegateOutputMessage(OutputMessage);
        TxtMessage.Invoke(d, new object[] { message });
      }
      else
      {
        TxtMessage.AppendText(message + Environment.NewLine + Environment.NewLine);
      }
    }

    internal void RedirectConsoleOutput()
    {
      MyTextWriter = new TTMyTextWriter(this);
      Console.SetOut(MyTextWriter);
    }