Interesting question, though.

The tax laws are very specific about defining alimony as payments that end with the death of the recipient ex-spouse.  Termination upon death of the recipient is a critical part of the definition that makes this transfer of funds deductable to the payor and taxable to the payee.

Yet I wonder.... Can you get blood from a stone?  Can the estate of a deceased payor ex-spouse continue to make deductable alimony payments to a surviving recipient ex-spouse?  I checked the IRS Form 706 (Estate Tax Return) and didn't find any reference to alimony.