In this paper, the unequal error protection (UEP) capability of convolutional encoders, in terms of the separation vector, is studied from an algebraic viewpoint. A simple procedure is presented for constructing a generator matrix, which is basic and has the largest separation vector for every convolutional code. Such a generator matrix would be desirable, since the corresponding encoder not only achieves UEP optimality, but also avoids undesired catastrophic error propagation. In addition, canonical generator matrices, which are both basic and reduced, are even more preferable for encoding, since they attain the lowest complexity for Viterbi decoding. However, the direct transformation from a UEP-optimal generator matrix to a canonical generator matrix may come with an unexpected loss of the separation vector. We also propose a specific type of transformation matrix that reduces the external degrees of the generator matrices, from which canonical generator matrices can be constructed that include the mitigated degradation of the separation vector. Finally, beneficial UEP convolutional codes that achieve the maximum free distances for the given code parameters are provided.