*This is not a complete answer, but it shows one instance where unpublished notes by Paul Erdős resulted in a recent publication.*

Paul Erdős's notes on Egyptian fractions are with <A HREF="https://en.wikipedia.org/wiki/Ronald_Graham">Ronald Graham,</A> who has reproduced some of them in <A HREF="http://www.math.ucsd.edu/~ronspubs/13_03_Egyptian.pdf">Paul Erdős and Egyptian Fractions.</A> Graham mentions one unfinished manuscript in which "it is shown that any integer can be represented as a sum of reciprocals of distinct numbers which each have exactly three prime factors". This was only published in 2015, twenty years after Erdős's death. As this <A HREF="https://www.simonsfoundation.org/2015/12/10/new-erdos-paper-solves-egyptian-fraction-problem/">commentary</A> aptly notes *"Nearly 20 years after his death, the famed mathematician Paul Erdős keeps on publishing, thanks to the conjectures he left behind and the friends who strive to prove them."*

<IMG SRC="https://ilorentz.org/beenakker/MO/Erdos_1.png"/>

The <A HREF="http://www.math.ucsd.edu/~ronspubs/pre_tres_egyptian.pdf">2015 publication</A> by Butler, Erdős, and Graham ends with this comment: *"One of the authors believes that all rational numbers can be expressed in this form, another author has doubts that every rational number can be expressed in this form, and the third author, already having looked in The BOOK at the answer, remains silent on this issue."*