I am sorry your boyfriend is struggling so much. That is such a worry for you but it's good that he is gettnig help and that he has gained from that help. Your boyfriend has to slowly learn that when he has this overwhelming anxiety and it's connected to a challenge, which in this case is an assignment for the uni, he can acknowledge the fear and give himself permission to make the effort anyway and see how it comes out. The more he learns he can get past this anxiety and tackle challenges, the more he will make gains on dealing with that anxiety.
I struggle with PTSD, and I have had to deal with a lot of anticipation anxiety so I know it's a big challenge. I have made a lot of gains on it, and I was at one point suicidal and with that challenge, it very important to realize that while that desire may come up, it also goes away. Your boyfriend has to learn to be very patient and just keep on working at it and he will find that he keeps gaining on it.