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Recent data on the differential angular distribution for the transferreaction $^{11}$Li(p,d)$^{10}$Li at $E/A=5.7$ MeV in inverse kinematics areanalysed within the DWBA reaction framework, using the overlap functionscalculated within a three-body model of $^{11}$Li. The weight of the different$^{10}$Li configurations in the system's ground state is obtained from thestructure calculations unambiguously. The effect of the $^{9}$Li spin in thecalculated observables is also investigated. We find that, although all theconsidered models succeed in reproducing the shape of the data, the magnitudeis very sensitive to the content of $p_{1/2}$ wave in the $^{11}$Liground-state wave function. Among the considered models, the best agreementwith the data is obtained when the $^{11}$Li ground state contains a $\sim$31\%of $p_{1/2}$ wave in the $n$-$^9$Li subsystem. Although this model takes intoaccount explicitly the splitting of the $1^+$ and $2^+$ resonances due to thecoupling of the $p_{1/2}$ wave to the $3/2^-$ spin of the core, a similardegree of agreement can be achieved with a model in which the $^{9}$Li spin isignored, provided that it contains a similar p-wave content.

Description of the $^{11}$Li$(p,d){^{10}}$Li transfer reaction using structure overlaps from a full three-body model