How can I help him overcome his fear?
In short, encourage him to see a psychotherapist. Behavioral as well as systemic/strategic therapy have been repeatedly tested as effective methods for solving phobic problems.
People suffering phobic problems tend to use one or more strategies to ease the strain of their phobic responses, which - unintentionally and unconsciously - often maintain the phobic response.
Among these are avoiding, seeking assistance and preparing.
As a partner of somebody experiencing phobic problems, specially the „assistance seeking“"assistance seeking" response may affect you especially:
I can‘tcan't do X, but when you are with me, I can.
Getting assistance byfrom the other person is of course a sign of support and love, but at the same time sending an (unintended) message of
I am not capable to doof doing this on my own.
So in the short runterm, assisting will be experienced as a relief, but after that maintain the problem and makemakes it even worse by continually decreasing one’s expectations to beof being capable.
Encouraging your SO to face feared (but harmless) situations is surely helpful,helpful; assisting him in doing so might have adverse effects.
When seeing a psychotherapist, you might have a talk together to evaluate strategies to truly help your SO.