Are the children entitled to claim the apartment that the mother donated to a charitable organization, especially since she retained the right of usufruct until death, and the donation was not registered, especially given that the donation was intended to disinherit the heirs and the apartment represented most of the inheritance?

Dispute cases belong in the Sharia courts or to those who act on their behalf, due to their ability to hear from the parties involved in the dispute and issue a judgment based on that. A Mufti, however, only hears from one party.

To resolve this issue, reference can be made to what was written between your mother and the institution to ascertain the true intent of your mother: did she intend an endowment (waqf) and make its proceeds for herself throughout her life, which is permissible and binding? Or did she intend a gift contingent on death (hiba mu'allaqah bil-mawt)? The latter is a will (wasiyyah) and takes the rulings of wills.

A will is not executed for more than one-third of the estate unless the heirs consent. Some scholars have even ruled its absolute invalidity, even if the heirs consent. Accordingly, the heirs have the right to take whatever exceeds one-third of the total estate from the apartment. The institution would not have a right to the apartment except within the limits of one-third of the entire estate, including cash or any other assets of the deceased.