You have not stated that how the divorce decree was obtained in US?, whether it was a contested decree or by a mutual consent or an exparte decree?
If the divorce decree in US was obtained by either of the first two modes, then he is very safe and need not have applied for divorce again in India, because that decree itself is a valid decree dissolving their marriage and is recognised by Indian laws as a valid decree. However the exparte decree is not recognised to be a valid decree in India by its laws. Therefore, if the US decree was an exparte divorce decree, the present case in India is very much mandatory.
Thus, as per the pending divorce proceedings in India, there marriage is stll subsisting, therefore if he marries another girl during this time it will not be valid and is void marriage and also he can b booked for bigamy offences including the newly married wife, for the which the sentence, if convicted would be 7 years imprisonment.