What are the best ways to transfer money from an INR account to a USD account when the account holder now lives in the U.S.?

The person who owns the account can write to the bank and ask what would be a most acceptable method for the bank. Usually a bank will provide its own internal form that allows you to do such a transfer (if it can be executed). The owner of the account would have to autograph it and send it to the bank. There is a delay in this, mailing the form and and then mailing it back.