It is considered the problem of excitation transfer along a spin chain related to the applied problem of quantum computations. The model of a quantum system of interacting spins based on the Shr¨odinger equation with unbounded linear control is transformed to an equivalent derived system (known from the degenerate problems theory), and then approximately to derived systems of higher stages with reducing order. Their investigation performed analytically or via simple computations leads at least to approximate solutions and lower estimates of the transfer time, which can be used in subsequent improving procedures.