Once you select the edges and click on the connect button in the edit poly edges then this should close the hole, there is also bridge but sometimes this doesn't work because you have chamfed them, also if you go into border then you can choose the cap command this will cap the hole and you will need to do the same on the other side.
I'd probably delete the faces highlighted, and "remove" using cntr-remove, the leftover vertices. leave one vert so the big faces remain....and then take the verts and move them into the desired place and weld. If you don't care about smoothing, you can leave the n-gon that will result orthogonal to the chamfer. If you do care about smoothing you might want to add edges so that your polys are quads.
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