There are some papers in which "The higher infinite II" is given as references:
1) Forcing Axioms and the Continuum Problem -Sakae Fuchino
2) The mathematical development of set theory from Cantor to Cohen-Kanamori,
3) Distributivity properties on $P_\omega(\lambda)$-Matet.
But I have no idea about if the book is going to be published or not.
Even the following content is presented for the book (note that the book is a continuation of volume I, so it starts with chapter VI)!!!!
Chapter VI. Higher Combinatorics
Kurepa's Hypothesis and Chang's Conjecture
The Tree Property
Chapter VII. Forcing with Strong Hypotheses I
Master Conditions (Silver's upward Easton forcing,
Kunen's saturated ideal)
Ultrafilters (structure theory, combinatorics)
Singular Cardinals Problem (intro, Solovay's
result, ultrafilters, Silver's result)
Strong vs. Supercompactness
Singular Cardinals Problem Forcing (Magidor's earlier
Precipitous Ideals (combinatorics, equiconsistency
Chapter VIII. Covering and the Core Model
The Covering Theorem for $L$
The Core Model
Models and Mice
The Covering Theorems for $K$ and for $L[U]$
Applications of $K$
Chapter IX. Higher Combinatorics II
Reflecting stationary sets, Shelah's LM result, etc.
Chapter X. Forcing with Strong Hypotheses II
Radin forcing, Proper forcing, forcing axioms
Chapter XI. Consistency Results about AD