A catch-and-engage tool conveyed with a well casing for use in a wellbore comprising an outer housing having flow ports therethrough, a functioning apparatus disposed within the outer housing comprising a movable member/sleeve and a holding device, a blocking apparatus disposed within the outer housing comprising a blocking member configured to block one or more flow ports in a first position, a seating apparatus positioned upstream of the blocking apparatus configured to form a seat in the tool. When a ball deployed into the well casing passes through the tool in a downstream direction and moves back in an upstream direction, the restriction element engages onto the holding device and moves the movable member such that a port in exposed to uphole pressure and the blocking member travels to a second position in a reverse direction unblocking flow ports and enabling fluid communication to the wellbore.