life insurance policy, failure to update beneficiary, FL state law

Your problem is the very reason people are wise to retain all proof of beneficiary changes. Insurance companies have many changes in employees (and sometimes ownership) over the long period of time that they operate. It is important to note that this matter should be addressed quickly, before any monies are paid out to the prior beneficiary. This is something that a probate attorney should be able to address with you. The attorney may be able to get the insurance company to hold any payouts until the matter is sorted out. If not, it may require a court order. Questions I would ask are whether the documents you have were ever sent into Sears and if you have proof that Sears received them. If Sears sent out the confirmation letter, and it can be proven to them, they should honor it. Though most life insurance issues are resolved without attorney involvement, in a case such as this, it may require an attorney's knowledge and expertise in order to succeed.

You write that you "have the confirmation letter and a copy of the beneficiary," but we cannot tell what that means. Do you have a copy of the letter that she sent to Sears? Do you have a copy of the letter that Sears sent back confirming that it received the change of beneficiary form? The latter is, of course, more helpful than the former. If you have your grandmother's signature on a change of beneficiary form, was it witnessed by someone?

In any event, you need to contact a probate attorney or a litigator immediately. This may not be something that a probate attorney can handle. It may be something where a litigator needs to sue the insurance company. It is not that the insurance company has done anything wrong, necessarily. It is just that with the suit filed, the insurance company will go to the court and, effectively say to the court "tell us what you want to do with this." That is (I'm speaking as a layman here since I'm a tax lawyer), I believe, referred to as an interpleader action.

Again, get to a probate attorney or litigator IMMEDIATELY. Do not handle this yourself.

Consider writing the insurance company, which probably is not the same as Sears, and make a claim by the intended new beneficiary for the proceeds. Your papework is the support for this claim. That will force the insurer to hold up any payment until the matter is resolved. You might then need a lawyer, or the old beneficiary might not contest anything.