From the official website:

>> The Home Office will retain the information it gets from test centres for a reasonable period. However, you should submit your application as soon as possible after taking the test.

In other words, Home Office states they will keep the test results for a reasonable period so taking it too early may cause problems. Does anyone know how long this “reasonable period” is? For example, I can only apply for the citizenship at the beginnin of Sept. I am wondering how early I can take the test in order to keep the result valid for the Home office for my Sept. application. I am thinking to take it the end of May or early June. I don't know whether this is too early? Any suggestion will be highly appreciated.

Yes, you can. You’ll be asked before taking the test which edition you studied, that's until the 3oth of June, check this post http://www.lifeintheuk.org/mod/forum/search.php?search=june&id=1

As of when you should submit you application, I don’t think it matters, you’ll get the passing certificate as prove to submitted with your application, saying that if any changes would be made, which’s more likely it would happen “i.e 3rd edition of the book lol” I don’t think your pass would be valid.

Best of luck