Is it just the base, Tomas? Or did the whole center rot out?

What I would do is to clean out any rotten tissue from the base and let the wound harden off a bit. You can dust it or dip it in a fungicide too if you want to. After a few days, put it into a pot with just perlite, and keep it just lightly moist. Perlite stimulates root growth and drains well. You don't have to fill the pot completely, just an inch or two at the bottom of the pot is enough. The pot will hold the mother upright (if the center hasn't rotted, you can continue keeping it filled with water) while it gives the pups a chance to form their own roots.

Thank you Lisa, everything will be done. The center looks healthy and firm.

Tomas