When I use "Highlights & Shadows" to lighten parts of an object that are cut off by a shadow boundary, I found it useful to turn off the "edge detection" and to set the brush range to "All". With the "Detect Edges" option on there will be a nasty darker line along the shadow boundary, and the width of this line will depend on the softness of the brush - the softer the brush, the wider the gap close to the edge that brush will not effect. The same goes for "Brush range: Shadows". To see the width of the gap I usually check with the brush overlay turned on.
Here is an example of an australian crocodile with the tail cut off by the shadows and a second screenshot showing the brushstrokes in red, with edge detection on. Notice the gap along the shadow boundary?

Also, with shadows this dark, you'll be out of luck with the "Highlights & Shadows" brick, if you want to remove the shadow completely. With this control you only can enhance the contrast a little and somewhat lighten it, but you cannot remove it. The sliders are limited to settings resulting in subtle effects.
(Fwiw, "Highlights & Shadows" follows the naming misleading naming conventions one finds everywhere in photography: it is more properly the "Lights and Darks" Brick.)
How right you are, Kirby!
P.S: I still have not managed to give the poor crocodile back its tail. Can crocodiles regrow their tail like lizzards?
The best I could do so far has been to use the "Curves" to raise the luminance and to stretch the contrast at the same time, but it looks very unnatural.
Message was edited by: leonieDF added second image and P:S: