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The differential cross sections of $^{7}\mathrm{Li}_{\mathrm{g}.\mathrm{s}.}, ^{6}\mathrm{Li}_{\mathrm{g}.\mathrm{s}.}, ^{6}\mathrm{Li}_{3.56}, ^{6}\mathrm{He}_{\mathrm{g}.\mathrm{s}.}$ reaction products emitted in the $^{7}\mathrm{Li}+^{10}\mathrm{B}$ collision are presented, measured for the first time in a single experiment under the same conditions. The measurements were performed using a $^{7}\mathrm{Li}$ beam at ${E}_{\text{LAB}}=58$ MeV from the U400 cyclotron at the FLNR, JINR, Dubna. The differential cross sections of $^{7}\mathrm{Li}_{\mathrm{g}.\mathrm{s}.}, ^{6}\mathrm{Li}_{\mathrm{g}.\mathrm{s}.}, ^{6}\mathrm{Li}_{3.56}$, and $^{6}\mathrm{He}_{\mathrm{g}.\mathrm{s}.}$ were measured in the angular range ${11}^{\ensuremath{\circ}}&lt;{\mathrm{\ensuremath{\Theta}}}_{\text{CM}}&lt;{84}^{\ensuremath{\circ}}$. The angular distributions of the measured differential cross sections were analyzed using the finite-range-coupled reaction-channel approach. The theoretical analysis provides a fair description of the measured $^{6}\mathrm{Li}({0}_{1}^{+})+^{11}\mathrm{B}_{\mathrm{g}.\mathrm{s}.}$ channel cross section, when the breakup process of the $^{6}\mathrm{Li}({0}_{1}^{+}$) excited state is explicitly included in the coupling scheme. It is demonstrated that the halo structure of $^{6}\mathrm{He}$ and its connection to the narrow resonance (the ${2}^{+}$ isobaric excited state of $^{6}\mathrm{He}$ formed in the one-proton stripping reaction) play a decisive role in describing the measured angular distribution for the population of the ${^{6}\mathrm{He}}_{g.s.}({0}^{+})+{^{11}\mathrm{C}}_{g.s.}(3/{2}^{\ensuremath{-}})$ channel.