They have to give him copies of his personal data, but not if it is also personal data relating to another individual who has not given their consent. Is it feasible for them to give him WhatsApp messages without identifying other people? Do you know they keep all those WhatsApp messages anyway?
If he is aware of gaps he should write specifying what he feels is missing. Ultimately he could complain to the Information Commissioner's Office if he feels they are not fulfilling the request.