He has put this idea in his head but can't prove any of it, so likely a therapist will be the best option. Since that hasn't worked, then he could try another one to see if he can relate to that person better.
Or maybe see someone like a preacher who has his own views of afterlife. Preachers like to talk about that kind of thing and it won't cost money.
Most people who are thoughtful, and many many people are not, can become obsessed with these kinds of thoughts. This one is fairly common. I even had it at a couple times in my life. If you think enough about life, there's an awful lot in it that can be scary. It can also be motivation for doing things. Most people, however, don't obsess to this level. His anxiety is moving toward OCD, and he's at an age near when this type of problem emerges. I don't know what kind of therapist he's seeing -- he needs one who specializes in treating anxiety -- most don't. Now, this could just be a phase in a young person's life that will pass. It could end up being fuel for a creative life. It could end up blocking him at every turn. Therapy requires him to work hard and a therapist who gives work to do -- just chatting doesn't necessarily help. If one therapist doesn't work, try another -- it's more of an art form anyway. As for you, there's not an iota of anything you can do to help him. Right now, you're enabling him most likely more than anything else because he's very young. The best thing you can do is treat him the same as always because you can't fix him, you don't have the tools or expertise and you're too close, but you can be there for him and you can keep pushing him to see he's thinking too much about this question that has no known answer -- none of us knows what it's going to be like after death. Religious people can offer him their blind faith, but if it isn't his blind faith, it won't help, but there's a reason so many have blind faith -- being blind to these questions takes them off the table. That's a comfort to many, but it does leave a lot of problems unresolved century after century.
This is really long but I figure you want some serious help here and thus won't mind that I have had to break this into several posts because of it's length. I'm new here so will know from now on to keep my posts much shorter; but I'm a writer and researcher in health psychology and also have a long history of horrendous anxiety, so...
I have quite a lot of potentially useful stuff to say on this subject, covering numerous things such as the five stages of sleep (only one of which is considered proper dream sleep - the weird state we go through when falling asleep, which is stage one, is the hypnogoigic state and is when we often experience very odd dream-like experiences; and everyone has had that senseation of falling and snapping back to fully awake with a sense of alarm; that's known as a hypnic or hypnogigic jerk). I'll say a bit about different types of therapy and what might be most appropriate; and I'll offer some suggestions about how you might be able to help. But it's almost 5am here in the UK and I need to sleep myself, so I'll ask some questions which will enable me to give more directed and thus hopefully more useful answer:
So, to the best of your knowledge:
1, What, if any, are your boyfriend's religious or spiritual beliefs? It will really help to give specifics about denomination, how religious are/were his parents; e.g., was he raised in a strict religious environment; was there fear and/or punishment involved etc etc.
AND CRUCIALLY: is his belief that the afterlife is total non-existent oblivion or is it being trapped, perhaps able to observe but unable to communicate? This is the most important point to clarify because if it is the former it is straight existential terror and might be fairly straight forward to resolve - though it could take some time it need not necessarily be complicated.
2, because it sounds like there could be separation anxiety and abandonment issues involved, is there anything notable in his background such as parents being divorced, having a sibling who was really ill when he was very young and thus he felt ignored whilst his parents were at the hospital all the time for two years?
3, When did this actually begin; did anything specific happen to trigger it; does he have a history of sleep disturbance? is it constant or does he have better and worse days? Can he sleep better in the day?