Is a marriage conducted without the father's knowledge but with the maternal grandfather's consent as a guardian valid in Islamic law? If not, what is required, given that the father has passed away?

The father is the most entitled person to marry off his daughter. If he is absent with a severed absence (غيبة منقطعة), the right transfers to the paternal grandfather. Ibn Qudamah defined a severed absence as one that cannot be ended except with great difficulty and hardship. Marrying a woman without a wali (guardian) is invalid, and the maternal grandfather is not among the awliya' (guardians). Since the father's right to guardianship is not forfeited by his marriage to another woman or his failure to inquire about his daughter, the aforementioned marriage is invalid. The marriage contract must be renewed with the closest guardian acting as wali, or the judge if no guardian is available, or an upright Muslim man if neither a guardian nor a judge is available. The two children will be attributed to their father and bear his lineage.