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[en] A single atomic field state is used as a quantum channel to teleport a state of two-qubit system. The possibility of estimating the teleported initial state parameters is discussed by means of quantum Fisher information. It is shown that by controlling the initial atomic field parameters, one may freeze the quantum Fisher information of the teleported parameters. Meanwhile, the teleported state keeps its local information. The sizes of the frozen areas depend on the initial state settings and the atomic field parameters. We show that the estimation degree of teleporting a single qubit is larger than that depicted for two-qubit system. Moreover, the estimation degree increases in the resonance case. It is shown that the maximum bounds of the quantum Fisher information are reached periodically. The phenomena of the sudden changes of quantum Fisher information are displayed at larger values of detuning parameters and the number of photons inside the cavity.