If she was the HSA participant, I don't see how it would be permissible for her executor to make a contribution on her behalf to her HSA after her death. I would expect the reasoning to be largely the same as that that led to the IRS has stating that the executor is not permitted to make a regular IRA contribution on behalf of a decedent. Additionally, by operation of law the HSA ceases to be her HSA upon her death, either becoming her spouse if her spouse is the beneficiary or ceasing to be an HSA entirely if the beneficiary is not her spouse, so there would be no HSA that could receive any HSA contribution made on her behalf.
