Back Court Situation

[FishinRef]

A1 establishes frontcourt status and has the ball stolen by B1. B1 is now in his backcourt with control. As B1 is nearing the division line, A1 tips the ball from B1 and causes the ball to go into B’s frontcourt, If A1 tipped the ball while in B’s backcourt, can A1 retrieve the ball in A’s backcourt?...........

My first opinion was that if A touched the ball last in his/her front court, they can not be the first to touch the ball in the back court. The fellow official who was working the game said he thought that A had never
re-established possesion or control in A's front court, so he thought that A could retrieve the loose ball. I don't have my books with me, so I will question the Refereeing Guru's of the world....

Legal or not??????