  Quantum Teleportation is a very useful scheme for transferring quantum
information. Given that the quantum information is encoded in a state of a
system of distinguishable particles, and given that the shared bi-partite
entangled state is also that of a system of distinguishable particles, the
optimal teleportation fidelity of the shared state is known to be
$(F_{max}d+1)/(d+1)$ with $F_{max}$ being the `maximal singlet fraction' of the
shared state. In the present work, we address the question of optimal
teleportation fidelity given that the quantum information to be teleported is
encoded in Fermionic modes while a $2N$-mode state of a system of Fermions
(with maximum $2N$ no. of Fermions -- in the second quantization language) is
shared between the sender and receiver with each party possessing $N$ modes of
the $2N$-mode state. Parity Superselection Rule (PSSR) in Fermionic Quantum
Theory (FQT) puts constraint on the allowed set of physical states and
operations, and thereby, leads to a different notion of Quantum Teleportation.
Due to PSSR, we introduce restricted Clifford twirl operations that constitute
the Unitary 2-design in case of FQT, and show that the structure of the
canonical form of Fermionic invariant shared state differs from that of the
isotropic state -- the corresponding canonical invariant form for teleportation
in Standard Quantum Theory (SQT). We provide a lower bound on the optimal
teleportation fidelity in FQT and compare the result with teleportation in SQT.
Surprisingly, we find that, under separable measurements on a bipartite
Fermionic state, input and output states of the Fermionic teleportation channel
cannot be distinguished operationally, even if a particular kind of resource
state with `maximal singlet fraction' being less than unity is used.
