Male cats are territorial. Female cats are hunters/providers. Neutering doesn't change this. Nor does it, (as I was dismayed to discover after having both my cats neutered), prevent either gender from spraying to leave messages for other cats. Those generalizations aside, each gender will defend territory, or hunt, when she or he feels inclined to do so.

"My frriend's cat sometimes needs to go thru the Burmese's garden to get to and from."

If your friend's cat is going onto the other cat's garden, why is your friend complaining about the other cat coming into her cat's garden?   You've used the terms, " being annoyed" and "frightens", but I haven't read any indication that the neighbour cat is actually attacking your friend's cat. Does it? Maybe your friend's cat is behaving wisely in cat fashion when he gives way to the other cat?

If the two cats are going to continue to share the same territory, (the combined yards, which both seem to feel free to use), they will have to sort it out themselves, without interference from your friend. Your friend's cat may not end up being the dominant one. If she can't accept that, she'll have to devise means to prevent the other cat from entering her yard when her cat is outdoors, or stay with her cat when he is out. In any case, she'd be wise to prevent her cat from wandering as there are many other dangers which can cause him more harm than the neighbour's cat will.