I plan to claim these also at the end of the year but can anyone help me out as to what I must do if I were to claim it here in the US?
I seriously have no idea what I must do after I get the shares.
As long as you only "own" shares, there should be nothing to worry about.
Simply ask at your local bank if you have to do any registering in regards to owning private international shares.
When/If ZPH starts to rake in the millions, and they start to pay you dividends, then you will have to declare them in your tax-form.
If you place your shares with your private bank, like I will be doing, then they will handle all that for you if you ask.