When does the obligation to pay Zakat al-Fitr for an absent slave arise if the master was previously unaware of the slave's continued life?

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If a master doubts the continued life of a slave whose news has ceased, Zakat al-Fitr is not obligatory because the continuation of ownership is unknown, and freeing such an individual for expiation would not be valid. However, if years pass and the master then learns the slave was alive, the master must pay the Zakat al-Fitr for all the past years. This is because the prerequisite for the obligation is established to have existed in the past period, thus requiring payment for those past years, similar to when news of the destruction of absent wealth is later found to be false.