  The procedure underlying the matching of 1-form (tetrad) fields in theories
possessing absolute parallelism -- f(T) gravity being within this category --
is addressed and exemplified. We show that the remnant symmetries of the
intervening spaces play a central role in the process, because the knowledge of
the remnant group of local Lorentz transformations enables one to perform
rotations and/or boosts in order to $\mathcal{C}^{1}$-match the corresponding
tetrads on the junction surface. This automatically ensures the continuity of
the Weitzenb\"{o}ck scalar there, even though this proves to be just a
necessary condition in order to obtain a global parallelization of the
spacetime.
