I would very much like to help you; it's just that with the scarce amount of information available to me I may not be the best judge of the situation.
I used to teach English to learners of all levels up to and including the FCE preparation course. I worked for a private language college offering evening classes available to the public. That meant that my students were persons of all walks of life, with vastly varying general education, background, occupational status, age and ... MOTIVATION.
I frequently encountered individuals who, similarly to the case you describe, thought that, once they'd reached a certain level of competence in English, there was very little they would to do to raise it even higher. It happened very often that such persons changed their attitude when confronted with a sample exam for one of the Cambridge certificates, depending on the level they represented at that time. Invariably, it was a humiliating experience even for those who regarded themselves as quite proficient simply because they were one of the top students in their grammar school's English class.
Preparation for a Cambridge exam, at least here where I live, is perceived by many as a naturally evolving phase of English education. Moreover, it poses a challenge which in itself can provide students with ample motivation to go further in development of their language skills. Cambridge examinations preparation courses are well structured, and the modern coursebooks are interesting enough to attract the learners' attention and keep them busy for some time, even if they eventually decide not to sit the exam session.
The fact that the preparation course students have a clearly set goal is not to be neglected, too.
FCE has become particularly popular here in Poland, even among secondary school students. Many of them even think CAE is the way to go because 'nowadays everyone's got the First Certificate' (an exaggerated statement, to be sure, but a motivating one, no doubt.)
Excuse my rambling on without end. I don't know what the availability of Cambridge exams is where you teach, but if there's any chance to go to such length, try to get the individual you refer to in your post interested in taking some exam-biased sample tests. They will at least indicate which particular language skills are not his strongest points, and may encourage him to work harder to improve those left behind skills.
Good luck in whatever path you choose to follow.