Here's an again super rudimental example - click on the stage will invoke the "save file as..." dialogue.

package {
    import flash.display.Sprite;
    import flash.events.MouseEvent;
    import flash.net.FileReference;
    import flash.utils.ByteArray;
    
    import org.alivepdf.fonts.CoreFont;
    import org.alivepdf.fonts.FontFamily;
    import org.alivepdf.fonts.IFont;
    import org.alivepdf.layout.Orientation;
    import org.alivepdf.layout.Size;
    import org.alivepdf.layout.Unit;
    import org.alivepdf.pdf.PDF;
    import org.alivepdf.saving.Download;
    import org.alivepdf.saving.Method;
 
    public class PDFDemo extends Sprite {
        private var _pdfByteArray:ByteArray;
        
        public function PDFDemo():void {
            var pdf:PDF = new PDF(Orientation.PORTRAIT, Unit.MM, Size.A4);
            var helvetica:IFont = new CoreFont(FontFamily.HELVETICA);
            pdf.addPage();
            pdf.setFont(helvetica, 24);
            pdf.writeText(24, "Hello World!");
            _pdfByteArray = pdf.save(Method.LOCAL, null, Download.ATTACHMENT);
            
            stage.addEventListener(MouseEvent.CLICK, click);
        }
        
        private function click(e:MouseEvent):void {
            new FileReference().save(_pdfByteArray, "hello-world!.pdf");
        }
    }    
}
 

Have you imported FileReference class? Also your code is missing the parentheses. You could of course write it like this as well:

        private function click(e:MouseEvent):void {
            var file:FileReference = new FileReference();
            file.save(_pdfByteArray, "hello-world!.pdf");
        }

This was very helpful! Now, what I would like to do, is automatically save a copy of that same pdf to a folder of my choosing in the same level as the create.php file.  It's great that the user has a copy but I'd like a copy of it myself. Is that possible?