  In this article, a sequel to "Global Frobenius Liftability I"
(math:1708:03777v2), we continue the development of a comprehensive theory of
Frobenius liftings modulo $p^2$. We study compatibility of divisors and closed
subschemes with Frobenius liftings, Frobenius liftings of blow-ups, descent
under quotients by some group actions, stability under base change, and the
properties of associated F-splittings. Consequently, we characterise Frobenius
liftable surfaces and Fano threefolds, confirming the conjecture stated in our
previous paper.
