The disclosed technology is directed towards an integrated short message service (SMS) function and short message service center function that delivers mobile terminated messages by selecting among access domains for to endpoints based on their capabilities, e.g., 5G, 5G+, LTE WI-FI, including multimode capabilities. The integrated SMS function determines attributes (e.g., capabilities) of a user equipment destination device for a mobile terminated message, obtains contextual data (e.g., current device reachability, network conditions) for the device, and determines which access and mobility management function (AMF) or mobility management entity (MME) is associated with the device. Based on the various obtained information, the integrated SMS function selects an appropriate access domain based on the capabilities and contextual data, and if the device is reachable, correctly routes the message for delivery. Retry operations can be set up for devices that are not currently reachable.