Why is your client angry?
Someone gave him the impression that the ODP was a listing service, that he could give someone money, and the ODP listing would happen within a particular time.
That is not the way the ODP works. Fortunately, your client learned the truth. And now he is angry at the person who led him wrong.
None of that matters much to us -- it is between you and your client how you apologize for making promises you could not keep, and telling him things about the ODP that aren't true.
There's nothing to "do" here. You can check the status in a month, to make sure your site suggestion was received OK (but it nearly always is.)
Eventually, an editor will find the site (perhaps because of your suggestion, perhaps another way), review it, and decide whether to list it. We don't know which editor that will be. We don't when that will happen.
We have no way of finding out when that will happen. We have no way of making it happen sooner. It will happen when some editor decides to do it. That's the way the ODP really works.
If you are looking for site review services, there are other places, reputable places, that offer that: Yahoo, for instance.