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We reanalyze the $B\to M$ tensor form factors in a covariant light-frontquark model, where $M$ represents a vector meson $V$, an axial-vector meson$A$, or a tensor meson $T$. The treatment of masses and mixing angles in the$K_{1A,1B}$ systems is improved, where $K_{1A}$ and $K_{1B}$ are the $^3P_1$and $^1P_1$ states of the axial-vector meson $K_1$, respectively. Rates of$B\to M\gamma$ decays are then calculated using the QCD factorization approach.The updated $B\to K^*\gamma$, $B\to K_1(1270)\gamma$, $K_1(1400)\gamma$ and$K_2\gamma$ rates agree with the data. The $K_1(1270)$--$K_1(1400)$ mixingangle is found to be about $51^\circ$. The sign of the mixing angle is fixed bythe observed relative strength of $B\to K_1(1270)\gamma$ and $K_1(1400)\gamma$.The formalism is then applied to $B_s\to M$ tensor form factors. We find thatthe calculated $B_s\to \phi\gamma$ rate is consistent with experiment, thoughin the lower end of the data. The branching fractions of $B_s\tof_1(1420)\gamma$ and $f'_2(1525)\gamma$ are predicted to be of order $10^{-5}$and it will be interesting to search for these modes. Rates on $B_s\tof_1(1285)\gamma$, $h_1(1380)\gamma$, $h_1(1170)\gamma$, $f_2(1270)\gamma$decays are also predicted.

B to V, A, T Tensor Form Factors in the Covariant Light-Front Approach: Implications on Radiative B Decays