migration notice esa to UC

Hello all, PLEASE HELP! My son has been given a deadline of 14 March to migrate to UC. CA have been very helpful with my questions, and will be helping him with his application, but I am not sure all the advice i have been given today is accurate? I really do not know how to decide the best time for him to apply. He has his esa payment going in on the 4th March, which means his next payment would be 18th March- 4 days after the deadline. i was advised that if he claims on 14th (the latest he can claim), he will still get his payment on the 18th AND another payment 2 weeks after making the UC claim- and his housing benefits covering 2 weeks after the claim date. I was under the impression that his ESA would be paid for one more time (eg, UP to 2 weeks) after claiming. I am very confused. I am trying to make this move as stress-free as possible for him and have everything we need in place before making the application. He is autistic and in the support group. He has full council tax relief and full housing benefit. i've scoured these pages but haven’t found the info I need. Thanks for any advice you can give me