We introduce the infinite-dimensional Lie superalgebra A{\mathcal{A}} and construct a family of mappings from a certain category of A{\mathcal{A}} –modules to the category of A₁⁽¹⁾{A_1^{(1)}} –modules at the critical level. Using this approach, we prove the irreducibility of a large family of A₁⁽¹⁾{A_1^{(1)}} –modules at the critical level parameterized by c(z) Î \mathbbC((z))\chi(z) \in \mathbb{C}((z)) . As a consequence, we present a new proof of irreducibility of certain Wakimoto modules. We also give natural realizations of irreducible quotients of relaxed Verma modules and calculate characters of these representations.