Generally speaking, income or business taxes died with him, you did not need to repay them. His estate has to pay any taxes before the rest of the estate is distributed to the heirs, but if there is not enough in the estate to cover the taxes, then they just don't get paid. If he has an estate that was divided among his heirs (other family or whomever), his final expenses should have been deducted from the estate before the rest was distributed. You would have to try to recover the taxes from the heirs who benefitted by your action. If there is no estate, then you should not have paid the tax and there is no way to get it back.
If you paid back taxes on land or property that you inherited (you now own it), that is deductible in the normal way of deducting property taxes. If you paid back taxes on inherited property that was sold and distributed to the heirs, the taxes should have been deducted from the sales proceeds before the leftover amount was distributed.
You may need to see an attorney.
