"The woman receives a horse from her husband."
Translation:Kvinnan får en häst av sin man.
So it seems like "från" is used when the emphasis is on the direction or origin of the item, or perhaps on the item itself, and "av" when the emphasis is on the "giving/receiving." That is, the distinction between "She received [a letter from her husband]" versus "She [received from her husband] a letter."
So in this particular sentence, the implication is "The woman receives-from-her-husband a horse" hence "av", as opposed to "The woman receives a horse-that-originated-with-her-husband."
It isn't a particle verb here. A lot of verbs work like this in Swedish – they (or, to be more exact, the same combination of letters) can be either a particle verb or a verb plus a preposition. The difference is clear in speech because the particle is always stressed and the preposition isn't. In this case it's clear in writing too because if av had been a particle, it would have had to stay closer to the verb.
But in some cases there can be misunderstandings, even very embarrassing ones. For instance stöta på is a particle verb meaning 'run into' but stöta på is a (somewhat informal) verb + preposition meaning 'come on to'. So in writing, you can't tell whether Jag stötte på min chef på stan means 'I ran into my boss in town today' or 'I came on to my boss in town today'.