Аннотация:A problem of an ambiguity in constructing conserved quantities in the framework of Teleparallel Equivalent of General Relativity is considered. A formalism based on the Noether procedure for constructing conserved currents and which is covariant with respect to both coordinate and local Lorentz transformations is studied. As a model for applications, a Schwarzschild black hole moving with constant velocity (with respect to distant static observers) is considered, for which conserved total energy and momentum are calculated. To avoid an ambiguity in such calculations an appropriate gauge defined by a pair of tetrad and related inertial spin connection has to be defined. Such a gauge is found and, as a result, acceptable (reasonable and unambiguous) conserved quantities are obtained. The found gauge is compared with previous ones. The results are related also to those obtained in the framework of well known Brown-York’s and Arnowitt-Deser-Misner’s formalisms.