var sourceFile = "text.txt";
var targetFile = @"C:\Users\Tomas\Desktop\MovieStarz\MovieStarz\WriteText.txt";
var id = App.Moviess.Filmerna[index].id.ToString();

var lines = File.ReadAllLines(sourceFile)
    .Where(l => l.Contains(id))
    .ToArray();

File.AppendAllLines(targetFile, lines);