From what I understand a propositional variable must represent a statement (either true or false). If so, eliminating free variables from any predicate by either:
(1) Replacing free variables with constants
(2) Binding free variables with quantifiers
should allow us to create statements in FOL that can be expressed in propositional logic (as long as these are named by propositional variables).
However, I remember reading somewhere that in propositional logic statements represented by propositional variables have to be about specific objects. For example, letting some $Q$ stand for "$Shoe_1$ is green" rather than "All shoes are green". So that if we had a finite, known domain in FOL, and wished to express the following statement in propositional logic:
$(\forall x) (x$ is a shoe $\wedge$ $x$ is green)
we'd have to convert it as: ($Shoe_1$ is a shoe $\wedge$ $Shoe_1$ is green) $\wedge$ ($Shoe_2$ is a shoe $\wedge$ $Shoe_2$ is green) $\wedge$ ... $\wedge$ ($Shoe_n$ is a shoe $\wedge$ $Shoe_n$ is green)
instead of letting some propositional variable $P$ stand for "All shoes are green".
Is this accurate? I'm a beginner so I apologize for any vagueness in the question. Thanks!