No. The only thing you can do with the inherited IRA is withdraw money and pay the tax. You can't convert it to another tax-free account in your name. Also, you can only do a funding distribution if you are eligible to make HSA contributions, meaning you have a qualifying HDHP, and have no other medical coverage such as Medicare.
If you are eligible to make HSA contributions, you could withdraw money from the IRA, pay the income tax, contribute an equal amount to the HSA from your own funds and take the tax deduction. That would offset the tax on the withdrawal. You just can't do it directly.
