Two examples of how to do it here
What if the wall is already there?
Oversized cut with a 9" angle grinder, trim the corner bits off and a sloppy mix of mortar around the box and then just squeeze it in?
But then you will have a problem with the DPM staying in place at the top of the box. It needs to act as a drip tray above the box before returning behind the box.
1968/9 build that had foam cavity wall insulation injected say 30 years ago?
Open to suggestions.