We have used low-temperature scanning electron microscopy for the investigation of the interaction of fluxons (Josephson vortices) with a superconducting (Abrikosov) vortex trapped in one of the electrodes of a long quasi-one-dimensional Josephson junction. The Abrikosov vortex penetrated a top superconducting film and spread out in the tunnel barrier area between the films. In addition, we were able to move the Abrikosov vortex across the junction by the electron beam and to measure at the same time the value of the critical current of the junction. A model explaining a critical-current dependence on the external magnetic field and on the Abrikosov vortex position is proposed. We have also observed the bound states of a fluxon trapped by the Abrikosov vortex in the Josephson junction.