  Pulsar timing arrays (PTAs) are designed to detect gravitational waves with
periods from several months to several years, e.g. those produced by by wide
supermassive black-hole binaries in the centers of distant galaxies. Here we
show that PTAs are also sensitive to mergers of supermassive black holes. While
these mergers occur on a timescale too short to be resolvable by a PTA, they
generate a change of metric due to non-linear gravitational-wave memory which
persists for the duration of the experiment and could be detected. We develop
the theory of the single-source detection by PTAs, and derive the sensitivity
of PTAs to the gravitational-wave memory jumps. We show that mergers of
$10^8M_{\odot}$ black holes are $2-\sigma$-detectable (in a direction,
polarization, and time-dependent way) out to co-moving distances of $\sim 1$
billion light years. Modern prediction for black-hole merger rates imply
marginal to modest chance of an individual jump detection by currently
developed PTAs. The sensitivity is expected to be somewhat higher for
futuristic PTA experiments with SKA.
