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This is the second part of a two part work in which we prove that for everyfinitely generated subgroup $\Gamma < \mathsf{Out}(F_n)$, either $\Gamma$ isvirtually abelian or its second bounded cohomology $H^2_b(\Gamma;\mathbb{R})$contains an embedding of $\ell^1$. Here in Part II we focus on finitelamination subgroups $\Gamma$ --- meaning that the set of all attractinglaminations of elements of $\Gamma$ is finite --- and on the construction ofhyperbolic actions of those subgroups to which the general theory of Part I isapplicable.

Hyperbolic actions and 2nd bounded cohomology of subgroups of $\mathsf{Out}(F_n)$. Part II: Finite lamination subgroups