  The obstruction for the existence of an energy momentum tensor for the
gravitational field is connected with differential-geometric features of the
Riemannian manifold. It has not to be valid for alternative geometrical
structures. A teleparallel manifold is defined as a parallelizable
differentiable 4D-manifold endowed with a class of smooth coframe fields
related by global Lorentz, i.e., SO(1,3) transformations. In this article a
general free parametric class of teleparallel models is considered. It includes
a 1-parameter subclass of viable models with the Schwarzschild coframe
solution. A new form of the coframe field equation is derived from the general
teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate
field strength $\F^a$. The field equation turns out to have a form completely
similar to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether
procedure, the source 3-form $\T^a$ is shown to be connected with the
diffeomorphism invariance of the Lagrangian. Thus the source $\T^a$ of the
coframe field is interpreted as the total conserved energy-momentum current.
The energy-momentum tensor for coframe is defined. The total energy-momentum
current of a system of a coframe and a material fields is conserved. Thus a
redistribution of the energy-momentum current between a material and a coframe
(gravity) fields is possible in principle, unlike as in the standard GR. For
special values of parameters, when the GR is reinstated, the energy-momentum
tensor gives up the invariant sense, i.e., becomes a pseudo-tensor. Thus even a
small-parametric change of GR turns it into a well defined Lagrangian theory.
