Dogs definitely pick up on your own nervousness. I used to pull Skye in and get up tight whenever we met a particular dog in the woods that Skye hated and would go for. As my ex pointed out, I was signalling to Skye that I was scared, this dog was trouble, and that therefore he needed to protect me - which he did very effectively!
Exactly so. I once had a GSDxLab who was absolutely lovely with everything except other male dogs, and with them he was the devil incarnate.

I found I had to watch him like a hawk, and when he approached another male dog, stay well clear, let them sniff and do the initial greetings, then just before the moment when Moses would strike a pose and say, "Go on then - make my day", I would have to call him away. If I called too soon, he'd have lost face so wouldn't come and if I left it a second too late, the other dog would have time to say, "Oh yeah? You and whose army?" and it would be a case of diving in to seperate them. (Incredibly, I only ever got bitten once doing this.)
A friend used to look after him when I was away, and Mose would always be worse with other male dogs when I got him back. I eventually discovered that the friend had been so frightened of his having a fight, she'd call him and leash him whenever she saw another dog in the distance, and then hold him really close, being very nervous, as the other dog passed. Of course what she transmitted to Moses was, "Other dogs are
really scarey and I need protecting from them."
I'd planned to have this dog castrated when I first got him - he was a rescue, we reckoned probably about 12 months old when I got him - but my vet friend (male! of course!

) had talked me out of it.
Well, Moses had now become almost unmanageable around other male dogs, even by me, so I decided to get him castrated anyway. It was explained to me that adult dogs produce testosterone in the adrenal glands in the kidneys as well as in the testes, so in some dogs castration later on in life may have minimal effect; it depends what proportion of his testosterone he produces in his adrenal glands. It takes quite a time for the levels to reduce, plus of course there are some learned behaviours / habits to unlearn, but in Moses' case, he did become quite a bit more placid over a period of about 12 months. I definitely did wish I'd had it done earlier - I'd been having to plan walk routes around where and when I
didn't expect to come across other male dogs for quite a few years, and, I realised once he'd calmed down, I'd never been relaxed when he was off-lead in case another dog appeared unexpectedly.
So I absolutely would suggest to this lady that she try castration. She surely won't breed from an animal with such a temperament quirk anyway, so she won't miss his nuts, and as long as she takes care with his diet so he doesn't get overweight, the worst that happens is she has a vet bill and not much difference. But if she's lucky, as I was with Moses, and her dog produces most of his testosterone in his testes and not much if any in his adrenal glands, she may end up with a dog that's a lot more of a pleasure to take for a walk.
Her vet may suggest that she could try an anti-testosterone jab to "see what the effect of castration would be like." I can't recommend this. The vet friend who condemned me to years of unnecessary hassle succeeded in his persuasion largely through getting me to try one of these jabs on Mose. The dog just basically slept for a month, listless, disinterested in anything, a great big flobby mound of blubber that was no fun to own. When in the end I did get him castrated, it made no difference to him at all in any respect except that he did gradually become less aggressive towards other male dogs.
Whether she has him castrated or not, the GSD's owner will need to do some socialising training with the dog and - more importantly - with herself handling the dog as well. The Breed Society should be able to tell you about trainers and clubs in your area.