When filling the hole you need to use some kind of "Backing" for the patch material.. Off hand I'd guess expanding foam is good as any.
I'm thinking, which of course is a dangerous thing for me to do...
Take fibergblass tape.. Glass it (Coat it with resin) poke a hole in it, "Stuff" it inside the hole then shoot foam in via the hole (Stick the nozzle tube through the hole) so the foam, as it expands, pushes the resin filled cloth tape against the back of the wall you holed. Layer one of the repair.
NOTE: Pay particular attention to the joke "Which of course is a dangerous thing" I have never tried this, do not know if it would work, do not know if it's a good idea, bad things might happen.. Or not.