This quest probably doesnt work. Tried it several times.

This last try was, when I intercepted him just two jumps away from my system. The slowes vessel is stolen ship with only 9 movement points.  Otherwise it would be only one jump.

And in every attempt, stolen hero ship was destroyed at the end of the first turn.

If it is meant to get ino owning system in only one jump, is there ANY way how to complete this?

I always go after this quest due to its awesome reward and to intercept the photbomber you have to wait until he moves. The location he is moving too you need to have your fleet there first and on gaurd. Also dont attack the photo bombers ship, only blockade the system he is in route too and boom. Success!

Add to @plutar advise: it normally moves in a limited number of systems, not in circles, but almost never out of a "comfort zone", so after a while you can guess more or less which system will move to.