  We examine various methods of constructing conserved quantities in the
Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in
the covariant formulation the preferred method are the Noether charges that are
true invariant quantities. The Noether charges depend on the vector field $\xi$
and we consider two different options where $\xi$ is chosen as either a Killing
vector or a four-velocity of the observer. We discuss the physical meaning of
each choice on the example of the Schwarzschild solution in different frames:
static, freely falling Lemaitre frame, and a newly obtained generalised freely
falling frame with an arbitrary initial velocity. We also demonstrate how to
determine the inertial spin connection for various tetrads used in our
calculations, and find a certain ambiguity in the "switching off" gravity
method where different tetrads can share the same inertial spin connection.
