Usually this happened when there was a sudden change on the environment. I had 2 succulents had similar to those, but for my case I was making a sudden change by moving the plants from shaded area to a very hot area, and those plants just can not get used to the new environment, the top area of the plant ( the soft and weakest part) just wrinkled and turn black.
You may try to check what kind of environment changes to that plant when moving from your mother's home to your sister's, and try to adjust on that area.
