Don’t waste your time to wait for the sending report from ETS. It will be sent to you by air mail. So, it takes much more time. When you received it finally, your score report might have been already sent to your school for quite a long time. Normally, it takes less than three weeks to arrive your school in slack time (September-November) and more than four weeks in peak season (December- next January).
I sent my GMAT and Toefl to five schools. Only one school replied after a week that it received my GMAT score. I don't know whether other four schools did it too. And no indication is released about toefl. Even ETS hasn't offered any test score delivering result to me. So what I can do is sending my photocopies of the tests to every school I apply.
But the school which I listed on the report request when I took the test, said that they received the test score on my application status check, including the time and the results.