private void SaveButton_Click(object sender, RoutedEventArgs e)
{
    string fileName = @"D:projectsPersonInfosFilesPersonInfos_Copy.txt";
    PersonInfosTable.ConvertToTXTFile(fileName);
}

public void ConvertToTXTFile(string fileName)
{
    StringBuilder sb = new StringBuilder();
    System.Text.Encoding Output = null;
    Output = System.Text.Encoding.Default;

    foreach (PersonInfos personinfos in PersonInfoDetails)
    {
        if (PersonInfos.SelectCheckBox == true)
        {
            string line = String.Format("L§" + personinfos.FirstName + "§" + personinfos.LastName + "§");
            sb.AppendLine(line);

            StreamWriter file = new StreamWriter(fileName);
            file.WriteLine(sb);

            file.Close();
        }
    }
}

public void ConvertToTXTFile(string fileName)
 {
     StringBuilder sb = new StringBuilder();
     System.Text.Encoding Output = System.Text.Encoding.Default;
     foreach (PersonInfos personinfos in PersonInfoDetails)
     {
         // Collect every personinfos selected in the stringbuilder
         if (personinfos.SelectCheckBox == true)
         {
            string line = String.Format("L§" + personinfos.FirstName + "§" + personinfos.LastName + "§");
            sb.AppendLine(line);
         }
     }

     // Now write the content of the StringBuilder all together to the output file
     File.WriteAllText(filename, sb.ToString())
}

if (personInfos.SelectCheckBox == true)
{
    // ...
}