No. If it is a sole proprietorship, the money belongs to that person, be it "him" or "her." Just because they want the spouse to be an authorized singer on the account, you should not assume that they automatically want the spouse to own the funds at the time of their death and enforce that assumption. The funds in an individual or sole proprietorship account will be controlled by the terms of the owner's will.
In some states, it is acceptable to name a POD beneficiary on a sole proprietor's account, because it is simply an individual account by another name. If that is what the customer actually wants and your state's laws permit it, fine.
And in some states, it's legal for a husband and wife to have a sole proprietorship that does not rise to the level of a partnership. It probably stems (my theory here) from traditional treatment (whether you agree with it or not) of the husband and wife as a unit, similar to the "tenancy by the entirety" form of ownership.
In these cases, I believe the surviving spouse gets the sole proprietorship assets, a will notwithstanding. But you should definitely check your state law on this point.
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