  For $p$ a prime number and $\mathscr{P}$ a $p$-equipped finite partially
ordered set we construct two different right-peak algebras (in the sense of
\cite{KS}) $\Lambda^{(r)}$ and $\Lambda^{(c)}$. We consider the category
$\mathcal{U}^{(r)}$ $\left(\mathcal{U}^{(c)}\right)$ consisting of the finitely
generated right $\Lambda^{(r)}$-modules ($\Lambda^{(c)}$-modules) which are
socle-projective. The categories $\mathcal{U}^{(r)}$ and $\mathcal{U}^{(c)}$
have almost split sequences. We describe he Auslander-Reiten components
$\mathcal{C}_{\mathcal{U}}^{(r)}$ and $\mathcal{C}_{\mathcal{U}}^{(c)}$ of the
corresponding simple projective modules in $\mathcal{U}^{(r)}$ and
$\mathcal{U}^{(c)}$. Then we prove that there is a bijective correspondence
between $\mathcal{C}_{\mathcal{U}}^{(r)}$ and
$\mathcal{C}_{\mathcal{U}}^{(c)}$, although the corresponding almost split
sequences have different shapes.
