Here's how I'd do this:
First delete the faces of one wall your original structure.
Then select the faces of the opposite wall and extrude them till the outer edge reconstructs the shape you want.
If you find it difficult to align the verts precisely, you can snap the 3D cursor to a vertex on the outer edge by selecting this vertex and Shift + S --> Cursor to Selected.
Then select the extruded faces and align them with that vertex by changing the pivot point to 3D cursor ., then scaling to 0 on the relevant axis (X in the example shown here): S --> X --> 0.
Now you need to delete the useless faces in between, so select and delete them or they will be non-manifold in the final mesh:
And finally, select all your vertices and remove doubles W --> Remove Doubles, to merge all the duplicate vertices created by the extrusion.