Little phatty - how to make the phatty play back the midi se

Hi, tthere! I have set up my sweet moog and I have the audio in and moog working as a midi controller but i would like now the moog to play back the midi once i correct it in the DAW(ableton). (so that moog will play the midi and I can record the audio in ableton. and so that i can add the appregiator in the DAW and moog will play the midi with the DAW’s appregiator - is that even possible??)

Any help would be great!

S xx