This question relates to commercial flights, typical two-pilot crew: In some airspaces, e.g. North Atlantic, pilots and Air Traffic Control use Controller Pilot Data Link Communication (CPDLC, datalink) to communicate instead of VHF or HF. Voice communication is ususally handled by the Pilot Monitoring (PM, or pilot non-flying PNF) - meaning the PM does the communication, and the PF executes instructions from ATC. With regards to CPDLC, which pilot handles datalink communication, is this also the PM as per standard operations? Are there standard operations for this?
With most airlines, the PM(pilot monitoring) handles datalink communication, with confirmation from the PF(pilot flying) before executing any instructions, clearances, or changes.
As with everything, there might be some exceptions at some airlines.