  We construct a homomorphism from the affine Yangian
$Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))$ to the affine Yangian
$Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n+1))$. We also give the
relationship between this homomorphism and the one from the affine Yangian
$Y_{\hbar,\varepsilon}(\widehat{\mathfrak{sl}}(n))$ to the universal enveloping
algebra of the rectangular algebra $\mathcal{W}^k(\mathfrak{gl}(2n),(2^n))$
constructed by the author.
