Finite Ramsey degrees and Fra\"iss\'e expansions with the Ramsey property

By a result of Zucker, every Fra"iss'e structure $\mathbf{F}$ for which the elements of $\mathrm{A}\mathrm{g}\mathrm{e}(\mathbf{F})$ have finite Ramsey degrees admits a Fra"iss'e precompact expansion ${\mathbf{F}}^{\ast }$ whose age $$\mathrm{A}\mathrm{g}\mathrm{e}$(\bf F^{*})$ has the Ramsey property. While the original method uses dynamics in spaces of ultrafilters, the purpose of the present short note is to provide a different proof, based on classical tools from Fra"iss'e theory.