uk benefits in eire

im going in circles as usual re my adult lads benefits- my lad currently gets esa and pip and has had no issues re claiming or payments- hes been offered a chance to live with an uncle in eire- will he still be able to continue his uk based claim or will he need to reclaim in eire after a wait- residency isnt an issue thanks to the common travel area- in or out of the eu- ive tried looking things up for him but get lost in the crossover of the terms used- 'abroad' and ,common travel area' and citizens advice cannot give a clear reply one way or the other.... thanks in advance