Can H1B Invest money outside USA?

While maintaining H-1B status you are only authorized to work for the employer who sponsored you, however, you may receive passive income from other sources. In other words, so long as you are not performing services or managing operations for the investment company within the U.S., then, yes, you should be able to invest your money in your home country.

As long as it is not a country with ties to terrorism, it would be no problem to invest your money as you wish. By way of example, I had a client, who thought he was donating to a charity to help victims of the tsunami, only to have the U.S. government determine that the donation actually went to fund the Tamil Tigers in Sri Lanka.

you can invest money anywhere you want as long as it is not a terrorist state (se us.dos.gov) you could buy shares of dell or apple or Credite Suisse. doesn't matter. good luck