No, you do not need corrected forms. Your W-2 is correct and includes both the compensation and the taxes withheld for the NQSOs vested. Morgan Stanley will not report your taxes withheld. Instead, you will adjust the cost basis so that you recognize 0 gain from the stock sale. At that point, both your compensation and your taxes withheld are only reported on the W-2.
If you sold all the shares that you exercised, then your cost basis would be the basis Morgan Stanley reported to you plus the amount reported to you as compensation on your W-2 in Box 12, Code V. For example, you sold $10,000 of shares the moment they became available to you. The fair market value was $10,000 but you only had to pay $7,500. The other $2,500 would be Code V on your W-2.
The basis would be reported on your 1099-B as $7,500 and you would have to adjust it for the $2,500 as compensation. Now you have a $10,000 sale with a $10,000 basis, so no additional tax from that transaction.
If you only sold half your shares, you would only adjust your basis by adding half the amount reported on your W-2 Box 12 code V.
Morgan Stanley will not re-issue a 1099-B with the correct basis, but you can adjust it on your tax form. TurboTax will automatically apply the correct coding to your tax forms to show that you are adjusting your basis.
You can also read this article to help you understand the tax treatment of either selling NQSOs right away or holding onto them so that the gains become long-term.
@Joshua_L
