Hats off to your friend for his honesty in discussing the problem.
Yes, I always felt a little anxious before take-off the first few times I went out on my own. Truth is that I always have felt a little anxious before take-off right from my hang-gliding days though thankfully never in the air (even when things have been going wrong).
My first few flights post PPL I felt especially anxious because I trained somewhere different from where I first struck out on my own. I was very nervous, and I think with reason, about flying in the London TMA.
I solved it firstly by flying more, because 'normalisation' can often help deal with anxiety caused by unusual circumstances. This doesn't have to be flying alone, unless this is a specific part of your friend's phobia. Secondly I did a few flights with an instructor, including tagging along for a ferry flight to a local airfield. Then I did some local flights. Then I repeated the cross-country by myself. Then I started branching out from there.
As others have said, a little anxiety is a good thing. A lot can be disabling. I hope your friend gets things worked out.