It is too late to file for any extensions ... just file the 2015 return asap. And next Jan you will need to also file a final personal return for the 2016 tax year and possibly an estate return as well.
Yes, the IRS will allows tax returns for deceased taxpayers (also called decedent returns) to be e-filed.
Before you file a decedent return:
1. Make sure the Social Security Administration has been notified of the taxpayer's death. You can either go to their website or call 1-800-772-1213.
2. To prevent an e-filing rejection, follow the instructions at this article that apply to the return.
Many (but not all) states allow decedent tax returns to be e-filed as well. We'll let you know when you get ready to e-file the state return.
How to efile for a
person who is deceased
You might need form 1310 to claim a refund for a deceased taxpayer
If your tax return is due a refund, you would not be able to e-File since Form 1310 requires that your Executor Letters Testamentary be filed with the return. I don't think TurboTAX would support such an attachment.
Also the article referenced would apply only to a spouse filing, not a personal representative.