It is bad taste and criminal to bilk the state. It is neglect of officials and citizenry not to question the strategy of corrupt officials who enrich themselves by creating privileged class for state officials. Serving the nation is not an enrichment scheme. It is a duty. If they do not care for the burden others are willing to take the load off their hands and do it fairly and transparently.
If there is no provision for a first lady when she served in that capacity and is entitled to it after her husband dies then one can logically conclude the living husband is presumed to be providing for her while he lived and they are still together. Consequently, if divorced the entitlement does not cease but persists. As long as the husband receives monies for his service the living divorced spouse is entitled to some percentage of his income.