What is the religious ruling on not carrying out a will left by a father to his daughter's children for one-third of the inheritance, knowing that the will is not documented, has no witnesses, was written four months before his death while he was ill and living far from the rest of his family, and that his daughter's children are well-off?

If the will fulfilled its legal conditions, such as having witnesses or your father's acknowledgment of it, then it is a valid will that must be executed, provided it is within the limits of one-third (of the estate) and for a non-heir. Its execution is not affected by the short duration, or by the father's illness, even if it was a death-bed illness, nor by its lack of official registration. However, if the will was in the father's handwriting, without witnesses, and he did not say, "Execute it," then it is not valid and shall revert to the general estate to be divided among the legal heirs.