  It is shown that for the restricted Zassenhaus algebra
$\mathfrak{W}=\mathfrak{W}(1,n)$, $n>1$, defined over an algebraically closed
field $\mathbb{F}$ of characteristic 2 any projective indecomposable restricted
$\mathfrak{W}$-module has maximal possible dimension $2^{2^n-1}$, and thus is
isomorphic to some induced module
$\mathrm{ind}^{\mathfrak{W}}_{\mathfrak{t}}(\mathbb{F}(\mu))$ for some torus of
maximal dimension $\mathfrak{t}$. This phenomenon is in contrast to the
behavior of finite-dimensional simple restricted Lie algebras in characteristic
$p>3$.
