It depends on what section of TurboTax you are referring to.
If you are in the Health Insurance section (link at the top), then you should put that you had health insurance all year (because you did). The Obamacare part you have to answer on your own.
If you are in the HSA interview and indicate that you had different coverage at different times of the year, then you would answer "yes" and then on the next screen, enter "none" for the first 9 months and "Family" or "Self" for the last 3 months, depending on what type of HDHP policy he had.
