Relatively easy:
1) in AZ Controller, "Options" tab, "Tweak current configuration..." select "Forget all assignments"
2) switch Arturia into MIDI mode, for encoders select absolute mode (so they produce 0...127 CC)
3) in the "Hardware" tab, assign MIDI to corresponding controls (see "Quick start" tutorial, so in general: turn/press control, select corresponding hardware control in AZC, press "Assign"). Note that you should assign Velocity messages from Pads, not Pressure. The second you can see (in the "Last MIDI event") if you press harder keeping the pad pressed. If possible, switch Pressure off in Arturia.
Things should work then, but not "perfect".
a) encoders can be used as "encoders" and not knob (so you do not have to adjust knobs to current value when switching channel). To do so:
a.1) configure Arturia to send encoder messages (not sure what the options are, but sure there are some)
a.2) "Forget"/"Assign" new messages for encoders (as in (3))
a.3) for each control, in the "Logic" tab, select "Value" Action and then "Endless" mode
Probably pads will not give the feedback (as on Lauchcontrol). Not sure if that is supported by Arturia (in the promo, they say "Red/Blue", just mode dependent).