We introduce the notion of ' s'-convolution in the hyperbolic plane $$ {\mathrm{\mathbb{H}}}^2 $$ and consider its properties. Analogs of the Helgason spherical transform in the spaces of compactly supported distributions in $$ {\mathrm{\mathbb{H}}}^2 $$ are investigated. We prove a Paley-Wiener-Schwartz-type theorem for the indicated transforms.