  A study of the B$^+$ $\to$ J$/\psi\overline{\Lambda}$p decay using
proton-proton collision data collected at $\sqrt{s} =$ 8 TeV by the CMS
experiment at the LHC, corresponding to an integrated luminosity of 19.6
fb$^{-1}$, is presented. The ratio of branching fractions $\mathcal{B}$(B$^+$
$\to$ J$/\psi\overline{\Lambda}$p ) / $\mathcal{B}$(B$^+$ $\to$
J$/\psi$K$^*$(892)$^+$) is measured to be (1.054 $\pm$ 0.057 (stat) $\pm$ 0.035
(syst) $\pm$ 0.011 ($\mathcal{B}$))%, where the last uncertainty reflects the
uncertainties in the world-average branching fractions of $\overline{\Lambda}$
and K$^*$(892)$^+$ decays to reconstructed final states. The invariant mass
distributions of the J$/\psi\overline{\Lambda}$, J$/\psi$p, and
$\overline{\Lambda}$p systems produced in the B$^+$ $\to$
J$/\psi\overline{\Lambda}$p decay are investigated and found to be inconsistent
with the pure phase space hypothesis. The analysis is extended by using a
model-independent angular amplitude analysis, which shows that the observed
invariant mass distributions are consistent with the contributions from excited
kaons decaying to the $\overline{\Lambda}$p system.
