Reversibility of quantum channels is a fundamental and special aspect of quantum dynamics, with unitary evolution serving as the most important prototype. Nevertheless, a broader class of reversible quantum channels exists beyond unitary channels, which plays an important role in quantum information processing. In the literature, reversibility of a quantum channel ${\cal E}$ usually refers to left-reversibility in the sense that there exists a quantum channel ${\cal F}$ such that ${\cal F}\circ {\cal E}$ is an identity channel. This amounts to employing the channel ${\cal F}$ to recover information loss caused by the quantum channel ${\cal E}.$ However, from both theoretical and practical perspectives, it is desirable to investigate whether there exists a quantum channel ${\cal D}$ such that ${\cal E}\circ {\cal D}$ is an identity channel. This amounts to encoding information via ${\cal D}$ and then subjects it to the quantum channel ${\cal E}$ for transmission or decoding. By analogy with the conventional (left) inverse, we call ${\cal D}$ a right-inverse of the quantum channel ${\cal E}$ if ${\cal E}\circ {\cal D}$ is an identity channel. In this paper, we investigate several structural characterizations for right-reversible quantum channels by establishing links between perfect-encoding channels and dual maps of the underlying right-reversible channels. We explicitly analyze the internal structure of such perfect-encoding channels and derive a decomposition theorem for them. Furthermore, we illustrate the structure via several examples, and discuss some implications of right-reversibility from the perspective of quantum encoding and error correction. We emphasize that the properties of left-reversible quantum channels cannot be readily transferred to those of right-reversible ones via duality since the dual (adjoint) of a quantum channel may not be trace-preserving and thus may not be a quantum channel (although still a quantum operation). These results offer potential applications for subsequent research on quantum dynamical control and quantum error correction.