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We work in the smooth category. Let $N$ be a closed connected orientable4-manifold with torsion free $H_1$, where $H_q := H_q(N; \mathbb Z)$. Our mainresult is a readily calculable classification of embeddings $N\to\mathbb R^7$up to isotopy, with an indeterminancy. Such a classification was only knownbefore for $H_1=0$ by our earlier work from 2008. Our classification iscomplete when $H_2=0$ or when the signature of $N$ is divisible neither by 64nor by 9.  The group of knots $S^4\to\mathbb R^7$ acts on the set of embeddings$N\to\mathbb R^7$ up to isotopy by embedded connected sum. In Part I weclassified the quotient of this action. The main novelty of this paper is thedescription of this action for $H_1\ne0$, with an indeterminancy.  Besides the invariants of Part I, detecting the action of knots involves arefinement of the Kreck invariant from our work of 2008.  For $N=S^1\times S^3$ we give a geometrically defined 1--1 correspondencebetween the set of isotopy classes of embeddings and a certain explicitlydefined quotient of the set $\mathbb Z\oplus\mathbb Z\oplus\mathbb Z_{12}$.

Embeddings of non-simply-connected 4-manifolds in 7-space. II. On the smooth classification