No, you don't pretend that you originally purchased the stocks by yourself. And doing that might make you pay more tax than you should. The tax return doesn't ask who the original purchaser was, but the fact that they were owned jointly affects your basis. Your basis affects the amount of profit or loss from the sale of the stocks, which affects how much tax you have to pay.
For each stock, half the shares were yours the whole time. The other half were your spouse's, and became yours when your spouse passed away. The basis of your original half of the shares is what you paid for that half. The basis of the half that you inherited is the fair market value on the date of your spouse's death. When TurboTax asks for your basis, you add the basis of the two halves together and enter the total.
If the stock increased in value from when you purchased it until your spouse passed away, your basis for your spouse's half of the shares will be higher than the original purchase price. That makes your gain (profit) from the sale lower, so you have less income to pay tax on. This is often referred to as "stepped up basis."
If you live in a community property state, and the stocks were community property, you get stepped up basis on the entire amount, not just your spouse's half. The community property states are Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, and Wisconsin.
