Formalise the following argument, then prove or disprove its validity:
Some psychologists admire Freud. Some psychologists like no one who admires Freud. Therefore some psychologists are not liked by all psychologists.
$\exists x(Px \land Fx)$
$\exists x(Px \land \forall y(Fy \implies -Lxy))$
$\therefore$ $\exists x(Px \land \forall y(Py \implies -Lyx))$
You have formalised the premises correctly.
The conclusion "Therefore some psychologists are not liked by all psychologists" sounds to me like it means "Therefore it's not that some psychologists are liked by all psychologists" rather than "Therefore some psychologists are disliked by all psychologists", so I would formalise it as $$\therefore \exists x(Px \land -\forall y(Py \implies Lyx))$$ instead.
P.S. Separately, observe that the argument is valid if formalised my way, and invalid if formalised your way.
Addendum
The given natural-language statement is ambiguous, so you're not really wrong; notice that if the author really intends the "disliked" interpretation then they would likely have written just that; what they wrote suggests that they mean the "not that" interpretation instead.