Free group on countable set is quotient-universal for finitely generated groups

Statement
Let $$\Omega$$ be a countable set, and let $$F$$ be the free group on $$\Omega$$. Then, every fact about::finitely generated group is isomorphic to some fact about::quotient group of $$F$$.

Related facts

 * Finitary symmetric group on countable set is subgroup-universal for finite groups
 * Free group on two generators is SQ-universal