Depends on the environment/equipment you're using.
ITB in Cubase or a similar DAW, I'd do something like record the "dry" signal in one track, then set up a send to a second track running a reverb insert set to produce a 100% wet signal, no dry component (the only 'verbs I've seen, HW or SW, that don't have that capability are stomp boxes for guitar/bass). Pan the two tracks left and right respectively and you'll get exactly what you want. You can also simply copy-paste the recording to the second track, but that makes edits harder as you have to make exactly the same changes to both tracks in order to get the right result.
OTB on an analog mixer it would be a similar idea; send a direct out to the reverb unit, set that to 100% wet, then bring the reverb output back to the mixer on a second channel, panned as desired.