On 25 August 2012 at 121.7 AU, Voyager 1 crossed the heliopause and measured a magnetic field with a strength of 0.4 nT in the very local interstellar medium (VLISM), while in the inner heliosheath it was 0.2 nT. The magnetic-field orientation was close to the spiral, and its direction did not change during the heliopause crossing. Simultaneously with the increase of magnetic-field magnitude at the heliopause, the number of energetic heliospheric particles and the temperature decreased substantially. At the same time, the Galactic cosmic-ray intensity enhanced together with the plasma density (from ≈ 0.002 cm −3 near the termination shock to 0.06 -0.08 cm −3 beyond the heliopause). If an increase of the density in the VLISM corresponding to a decrease in the temperature was expected, the strange behavior of the magnetic field causes doubt: did the heliopause-crossing take place? Here we suggest a dynamo mechanism as a possible reason for the observed magnetic-field behavior. We enumerate the necessary conditions for the dynamo process and analyze the Voyager 1 observations to test whether these conditions hold or not. We show that all preconditions are realized and estimate the energy of the dynamo action potential. We conclude that in principle, this process could work just beyond the heliopause, because differential rotation may exist in the nearest part of the outer heliosheath, in a layer where electric conductivity is high, but lower than the field-aligned conductivity in the surrounding regions and where the rotational kinetic-energy density is comparable with the observed magnetic-energy density. The latter circumstance corresponds to a requirement of dynamo action, for which kinetic energy of rotation provided by the Sun is an energy source for magnetic amplification.