  For a connected smooth proper rigid space $X$ over a perfectoid field
extension of $\mathbb{Q}_p$, we show that the Picard functor of
$X^\diamondsuit$ defined on perfectoid test objects is the diamondification of
the rigid analytic Picard functor. In particular, it is represented by a rigid
group variety if and only if the rigid analytic Picard functor is.
  As an application, we determine which line bundles are trivialized by
pro-finite-\'etale covers, and prove unconditionally that the associated
"topological torsion Picard functor" is represented by a divisible analytic
group. We use this to generalize and geometrize a construction of
Deninger--Werner in the $p$-adic Simpson correspondence: There is an
isomorphism of rigid analytic group varieties between the moduli space of
continuous characters of $\pi_1(X,x)$ and that of pro-finite-\'etale Higgs line
bundles on $X$.
  This article is part II of a series about line bundles on rigid spaces as
diamonds.
