  The single electron track-reconstruction efficiency is calibrated using a
sample corresponding to $1.3~\mathrm{fb}^{-1}$of $pp$ collision data recorded
with the LHCb detector in 2017. This measurement exploits $B^+\to J/\psi
(e^+e^-)K^+$ decays, where one of the electrons is fully reconstructed and
paired with the kaon, while the other electron is reconstructed using only the
information of the vertex detector. Despite this partial reconstruction,
kinematic and geometric constraints allow the $B^+$-meson mass to be
reconstructed and the signal to be well separated from backgrounds. This in
turn allows the electron reconstruction efficiency to be measured by matching
the partial track segment found in the vertex detector to tracks found by
LHCb's regular reconstruction algorithms. The agreement between data and
simulation is evaluated, and corrections are derived for simulated electrons in
bins of kinematics. These correction factors allow LHCb to measure branching
fractions involving single electrons with a systematic uncertainty below $1\%$.
