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Install a couple of 2x4s between the studs and a couple of 2x2s on the sides of the 2x4s so that the drywall can be attached to the top cut of the drywall.
Attach the drywall piece that you saved earlier with drywall screws.
Apply a thick layer of mud on the joint. Then apply drywall tape over the first coat.
After that dries, apply another coat. Spread the mud away from the joint so you can start feathering the seam.
Sand the joints down and blend the edges out.
Spray an aerosol textured drywall compound on the sanded wall. Let it dry out a little and then "knock it down" by placing a 12" knife and drag it in order to match the look of the closet wall. The great thing about working in a closet is that it doesn't have to match perfectly.
Tip: Whether your walls are faux finish or actual texture it is always best to practice the application a few times before you try to match the new application to the old.
Give the wall a new coat of paint, replace the trim molding and put everything back in place.