Funny, I am processing some of my photographs as we speak, and realized that halo (in my photos) comes from auto Highlights adjustment. I decided to sacrifice the highlights (i.e., bring them back to zero) in order to avoid such a pronounced halo. It worked for my photograph, not sure if it would work for anyone else's.
Slobodan, I recreated my b&w conversion with a virtual copy and was able to reduce the halo a bit. Again, as soon as I moved the highlight slider (reducing highlights), a halo began appearing. I also needed to use an adjustment brush to locally darken some sunlit surfaces, but tried to stay away from the circumference of the person's shadow as much as possible. In the end, the halo was less, but still present.
I don't use auto functions during processing exposure and I (try to) expose to not blow out highlights. First I process a color image, then convert to b&w using the "v" key (in LR) and further process for the monochrome version. Maybe this is a factor of having a Fujifilm x-trans sensor and using LR, but I won't change software or camera, so I'll keep refining my processing.