Il déteste le frère de _________.
(He hates the brother of __________)
This is a very good question, which I think the lesson should address.
My understanding is that whilst, grammatically, «Il déteste son frère» could be someone else's brother, in practice it would be understood as "He hates his brother" unless you have surrounding context to the contrary.
If you need to clearly refer to someone else's brother then you have to use a structure like the one Dawn suggests, with either à or de. If it's a (stress) pronoun, then you need to use 'à', if it's a name or noun, then you need to use 'de': https://www.thoughtco.com/french-possession-1368906
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