Q:

Does halogenation by phosphorus tribromide lead to an inverted product?

I think it follows the SNi mechanism and would not lead to Walden inversion.
Hence, the product should be (S)‐2‐bromobutane:

But the answer says otherwise (the problem didn't indicate the presence of pyridine in the reaction mixture though).

A:

Yes, the haloalkane product will have the inverse stereochemistry of the alcohol that it was produced form. $\ce{PBr3}$ does this by converting the $\ce{-OH}$ into a good leaving group and providing a nucleophile all in one. This is can be seen in the two step mechanism:
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When $\ce{Br-}$ ejects $\ce{PBr2OH}$ in an $\mathrm{S_N2}$ reaction, the stereochemistry is inverted:
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A:

Yes, halogenation by $\ce{PBr3}$ will lead to an inverted product, as it follows $\mathrm{S_N2}$ mechanism. In an $\mathrm{S_N2}$ mechanism, the product is formed through inversion as the incoming nucleophile attacks from the side opposite of the leaving group.

