Recent measurements of charm-baryon production in hadronic collisions have questioned the universality of charm-quark fragmentation across different collision systems. In this work the fragmentation of charm quarks into charm baryons is probed, by presenting the first measurement of the longitudinal jet momentum fraction carried by $\Lambda_{\rm c}^{+}$ baryons, $z^{\mathrm{ch}}_\mathrm{||}$, in hadronic collisions. The results are obtained in proton-proton (pp) collisions at $\sqrt{s}=13$ TeV at the LHC, with $\Lambda_{\rm c}^{+}$ baryons and charged (track-based) jets reconstructed in the transverse momentum intervals of $3 \leq p_{\rm T}^{\Lambda_{\rm c}^{+}} <~ 15$ GeV/$c$ and $7 \leq p_{\rm T}^{\rm jet\;ch} <~ 15$ GeV/$c$, respectively. The $z^{\mathrm{ch}}_\mathrm{||}$ distribution is compared to a measurement of ${\rm D}^0$-tagged charged jets in pp collisions as well as to PYTHIA 8 simulations. The data hints that the fragmentation of charm quarks into charm baryons is softer with respect to charm mesons, in the measured kinematic interval, as predicted by hadronisation models which include colour correlations beyond leading-colour in the string formation.