Several ways you can do this in Photoshop as usual, you could create a mask around just the shadow itself and use levels to lighten the shadow, but wall has a gradient from darker on the left to lighter on the right. I just created a mask for the entire wall then created a new blank layer with this mask. Now select a big soft brush and sample a colour from the darker area in the lower left and paint the left half of the wall, select a lighter colour from the far right and paint in from the right to mix nicely with the darker left side.
When you do this it pays to add a small amount of grain to the painted layer, this helps break up any banding you get with smooth gradients and also matches the grain with the wall on the far left of the image.
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