After you file

Yes.  I think you've misquoted the 1099-B by leaving out the word "basis", but the "proceeds" certainly are being reported to the IRS and the IRS certainly will be looking to see that the proceeds are included in your income tax return.  You enter the 1099-B's using the "Stocks, Mutual Funds, Bonds, Other" interview.

The basis of the stock, most commonly, is their fair market value at the date of death.  You need to look up that information if you don't have it.

You can use the "X" sales category.

Enter the 1099-B as it reads, leaving the date of acquisition and the basis fields blank.  Then click the "guide me step by step" button.  Click the "uncommon situations" button, click "stock", click "I inherited the stock."  Complete the rest of the interview.  The sales will be classified as "long term" irrespective of when your mother bought the shares or how long you owned them, as a matter of tax law.

Tom Young