So while remodeling a room, I've discovered that one of the exterior walls of my home has a hole in it that has apparently allowed water to get in and has rotted the plywood in the wall pretty badly. However, the damage is limited to the space between the corner and the first stud in the wall.

A neighbor has suggested simply filling the hole with spray insulation, cutting a new piece of plywood slightly larger than the damaged area, and securing it from the inside with liquid nails and coarse drywall screws. While it's appealing as a cheap fix, I don't think it's the best solution, but I'm not sure how to go about repairing it properly. Any suggestions? Pictures can be taken if they're helpful.