  We show that McVittie geometry, which describes a black hole embedded in a
FLRW universe, not only solves Einstein equations but also remains as a
non-deformable solution of f(T) gravity. This search for GR solutions that
survive in f(T) gravity is facilitated by a null tetrad approach. We also show
that flat FLRW geometry is a consistent solution of f(T) dynamical equations
not only for $T=-6H^{2}$ but also for $T=0$, which could be a manifestation of
the additional degrees of freedom involved in f(T) theories.
