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Heavy-flavor jets are powerful tools to gain insight into the in-medium partonic energy-loss mechanisms and the quark-gluon plasma's (QGP) transport properties in high-energy nuclear collisions. In this work we present the first theoretical study of the longitudinal momentum fraction $z_{||}$ carried by heavy-flavor mesons in jets in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. The p+p baseline is provided by POWHEG+PYTHIA8, which matches the next-to-leading-order hard processes with the parton shower. We employ a Monte Carlo transport model, which considers the collisional and radiative partonic energy loss, to simulate the evolution of heavy-flavor jets in the expanding QGP medium. We observe steeper $z_{||}$ distributions of $\rm{B^0}$ jets compared to those of $\rm{D^0}$ jets at the same kinematics region in p+p collisions, which may be a hint of the harder jet fragmentation function of b jets compared to c jets in vacuum. In A+A collisions, it is shown that the jet quenching effect would generally decrease the values of $z_{||}$. We have made a systematical study on how several factors, including jet $p_{\rm{T}}$, jet radius $R$, and collision centrality, would influence the medium modification of $z_{||}$ distributions of a $\rm{D^0}$ jet. In addition, we predict visibly stronger nuclear modifications of $\rm{B^0}$-jet $z_{||}$ distributions compared to a $\rm{D^0}$ jet within the same $p_{\rm T}$ windows as a result of the much steeper initial $z_{||}$ distribution of the $\rm{B^0}$ jet in vacuum.