Yes, you can - and should - put the correct purchase date for your stocks in TurboTax. After entering the sale info, click the blue button at the bottom, I'll enter additional information on my own.
On the page Let's get the rest of the info from your [Name] 1099-B, scroll down to the topic Corrected holding period and choose L - Long term (more than one year), then Continue.
Be certain you keep the supporting documentation with your return to prove your purchase dates, as using a different holding period can trigger a letter from the IRS.
