  This paper is dedicated to a further study of derived Azumaya algebras. The
first result we obtain is a Beauville-Laszlo-style property for such objects
(considered up to Morita equivalence), which is consequence of a more general
Beauville-Laszlo kind of statement for quasi-coherent sheaves of categories.
Next, we prove that given any (derived) scheme $X$, proper over the spectrum of
a quasi-excellent Henselian ring, the derived Brauer group of $X$ injects into
the one of the Henselization of $X$ along the base, generalizing a classical
result of Grothendieck and a more recent theorem of Geisser-Morin. As a
separate application, we deduce that Grothendieck's existence theorem holds for
the stable $\infty$-categories of twisted sheaves even when the corresponding
$\bbG_m$-gerbe does not satisfy the resolution property, offering an
improvement of a result of Alper, Rydh and Hall.
