Just to complete this trend, in case someone will have the same problem.
The fix was not that difficult. I removed the side cushion (pull and lift up) and got good access to the place in question from inside the cabin.

I used a strip of metal with two bolts and two nuts and drilled two holes in the car's metal plate that the bracket used to be welded to. There is plenty of space to work. I had to grind some edges of the broken bracket for a better fit.

There are probably other solutions as well, but you do have to drill a hole or two in the metal piece behind the side back seat cushion.