She has been issued with both Incentive Stock Options and Non-Qualified Stock Options in the U.S. parent which is listed on the New York Stock Exchange. The awards vest in equal portions over a 4 year vesting period
While the awards were originally granted to her when she was living in Singapore and relate to her Singapore service, the last three years of the grant will vest to her while she is living in NY.
Under U.S. law while these options will be Singapore sourced she will be subject to U.S. income tax treatment on the awards that vest to her after she arrives in the U.S. She will get a credit for any tax she has paid in Singapore (to the extent it is paid while she is a resident in the U.S.) and she will be liable for further tax in the U.S., the State of NY, and the NY city (to the extent the Incentive Stock Options and Non Qualified Stock Options) are taxable under U.S. law. Under U.S. law Incentive Stock Options and Non-Qualified Stock Options are taxable upon exercise, not upon vesting.
It is also important to note that while Incentive Stock Options are not subject to income tax on the spread (ie the difference between the grant price of the options and the market value at the time of exercise), they are subject to Alternative Minimum Tax. Whereas, Non-Qualified Stock Options are subject to income tax on the spread.