@roalddahl14 what I gather from your post is that :
(a) you are a Resident Alien for tax purposes --- you file your return on form 1040 ( supported by TurboTax ) and are taxed on your world income
(b) You have RSU ( or similar restricted stock grants ) from a foreign entity *( based in Singapore ). These are now restriction free (vested ). Assuming that you have not recognized these stocks ( either in Singapore , India or in US ), your basis is this is probably zero -- unless your employer at the time showed then FMV as income and was already taxed. Need details on this .
(c) Because you are Resident for Tax purposes and taxed on world income, when you dispose of these shares/ equity your gain is taxable income to the US. It is immaterial whether you are a Resident for Tax purposes or Immigrant ( GreenCard ) or citizen, you are still taxed on world income.
Hope this helps -- for more specific answer , please provide more details of the equity grant, basis, any taxes paid etc. etc.
I await your response
pk
