  The reaction $e^+e^-\rightarrow \Lambda^+_c\bar\Lambda^-_c$ is investigated
at energies close to the threshold with emphasis on the role played by the
$X(4630)$ resonance. The interaction in the final $\Lambda^+_c \bar\Lambda^-_c$
system, constructed within chiral effective field theory and supplemented by a
pole diagram that represents a bare $X(4630)$ resonance, is taken into account
rigorously. The pole parameters of the $X(4630)$ are extracted and found to be
compatible with the ones of the $X(4660)$ resonance that have been established
in the reaction $e^+e^- \to \pi^+\pi^-\psi(2S)$. The actual result for the
$X(4630)$ is $M = (4652.5\pm 3.4)$ MeV and $\Gamma = (62.6\pm 5.6)$ MeV.
Predictions for the $\Lambda^+_c$ electromagnetic form factors in the timelike
region are presented.
