This technique has fallen out of use for a full century and is only occasionally used any longer. Marvin Haggler used a variant of it to hunt down fleeing opponents. The shift jab is simple. As you jab, you step forward with the rear foot, effectively shifting your lead so you can mug your man from the side. It is a move with few opportunities against a fighter that moves well, which is the reason for its disuse. Fighters out of the Wild Card Gym are using the shift to score with pass hooks. Shifting with a jab could be a start to learning your pass hook.
The best reason to shift behind the jab is to cut a fighter off who keeps getting away to his left.
The term shift comes from fencing and was first used in boxing to describe a shifting shovel hook to the solar plexus thrown by Fitzsimmons to KO Corbett.
A simpler way to use the same concept is to throw the rear hand at a fighter moving wide to your right, and instead of resetting, shift that right foot forward and jab with the right, turning southpaw just long enough to catch him and bring him to bay. Once you get him against the ropes or in an exchange you can shift back to your orthodox guard.