So sorry for your loss.
Yes, you can file your son's tax return with TurboTax. You will want to create his own TurboTax account and create the return in his name. In addition, in the My Info section of TurboTax, section 3 will ask whether the return is being prepared for someone who is deceased. When marked YES, then a date of death can be entered. This will allow the return to be marked as a final return for a deceased person.
Also, here is some general information from IRS Publication 559 for Survivors, Executors and Administrators about filing a final tax return and who should sign the return.
Signature. If a personal representative has been appointed, that person must sign the return. If it is a joint return, the surviving spouse also must sign it. If no personal representative has been appointed, the surviving spouse (on a joint return) signs the return and writes in the signature area “Filing as surviving spouse.” If no personal representative has been appointed and if there is no surviving spouse, the person in charge of the decedent's property must file and sign the return as “personal representative.”
IRS Publication 559 Survivors, Executors and Administrators
