take some plumbers strap or a couple of brick ties, or similar, take a handy box like is there, screw the strap to the back of the box,
what you should have a box with some straps on the back side of it so there is some thing to anchor it with,
if you need to dig a little more of the adobe out then do so to get it to fit, and and if you have dug out behind the existing stucco a little so it will key in behind it.
attach the flex coming through the wall there to the best suited knock out of the box, put the box into the hole, take some coat hanger or wire and make a few V shaped rods, or used screws or similar, bend the strap and then pin or screw the straps into the adobe or use screws or what ever, some thing to hold the box in place, then mix up some sand and mortar cement, 3 sand to one cement mortar, or pre mixed) and plaster around it, if you need to do in layers (rough up the under coats so that the top layers have something to grip to, if you need to put some chicken wire around to support the surface, (like is in the stucco in the wall already), and work it up to level, if and then paint, and put the receptacle back in the box and a cover on the box, If that box pulls out it will have to take the entire patch with it, and if you have dug out behind the existing stucco a little so it will key in behind it , it would have to take out a section of the wall.
(I don't think you would really even need the straps but it would make it easier to hold in place and help secure it and key it in the mortar)
(NO I have never worked with adobe before, I have done a lot with stucco and mortar and block and so forth), I don't see why it would not work with adobe, since it is basically a mud block that is usuly stuccoed for a wall finish and to protect the dirt wall behind,
If I was doing the job this is how I would proceed, or in similar fashion, with out being there there may be some changes by space needs or practically but in general I would figure some way to support the box and hold it, who knows may be even some thing temporally attached to the cabinet, and then mud it in,
tape over the box to keep mud out of it,