In your DoWork event handler for the BackgroundWorker (which is where the background work takes place) there is an argument DoWorkEventArgs. This object has a public property object Result. When your worker has generated its result (in your case, a List<FileInfo>), set e.Result to that, and return.
Now that your BackgroundWorker has completed its task, it triggers the RunWorkerCompleted event, which has a RunWorkerCompletedEventArgs object as an argument. RunWorkerCompletedEventArgs.Result will contain the result from your BackgroundWorker.
example:
private void bgw_DoWork(object sender, DoWorkEventArgs e)
{
int result = 2+2;
e.Result = result;
}
private void bgw_RunWorkerCompleted(object sender, RunWorkerCompletedEventArgs e)
{
int result = (int)e.Result;
MessageBox.Show("Result received: " + result.ToString());
}