Thank you for your answers. So we were right, it's not good for that poor kitten.
My mother has already 2 cats and even if her heart is broken, she really can't take the kitten. I think at the end she will take her anyway, she just can't see an animal suffering. Actually we have think about trying to take the kitten and make it adopt without telling it to the neighbour. I know it is bad (shame) but that kitten could be killed or stolen anyway, she should just not leave it outside all the time if she doesn't want it to disappear