  The purport of quantum teleportation is to completely transfer information
from one party to another distant partner. However, from the perspective of
parameter estimation, it is the information carried by a particular parameter,
not the information of total quantum state that needs to be teleported. Due to
the inevitable noise in environment, we propose two schemes to enhance quantum
Fisher information (QFI) teleportation under amplitude damping noise with the
technique of partial measurements. We find that post partial measurement can
greatly enhance the teleported QFI, while the combination of prior partial
measurement and post partial measurement reversal could completely eliminate
the effect of decoherence. We show that, somewhat consequentially, enhancing
QFI teleportation is more economic than that of improving fidelity
teleportation. Our work extends the ability of partial measurements as a
quantum technique to battle decoherence in quantum information processing.
