C# How to redirect stream to the console Out?

Just point the stream to standard output:

sw = new StreamWriter(Console.OpenStandardOutput());
sw.AutoFlush = true;
Console.SetOut(sw);

Not that previous answer not correct, but since i do not have enough reputation level to add comment, just adding another answer:

If you would ever use pointing Stream to standard output as John proposed with using statement you should not forget to re-open console Stream later on, as explained in https://docs.microsoft.com/en-us/dotnet/api/system.console.setout?view=netframework-4.7.2

using (sw = new StreamWriter(Console.OpenStandardOutput())
{
    sw.AutoFlush = true;
    Console.SetOut(sw);
    ...
}
StreamWriter standardOutput = new StreamWriter(Console.OpenStandardOutput());
standardOutput.AutoFlush = true;
Console.SetOut(standardOutput);