The answer is: Yes, the ḥadith is authentic. Yet the individual whose provision is increased and whose life is prolonged because he maintains family ties was, from the outset, written as one who would keep those ties, whose provision would be expanded, and whose lifespan would be extended. The matter had already been fixed in that manner. Nevertheless, the Messenger ﷺ said, “Whoever would like his provision to be enlarged and his lifespan extended should maintain his ties of kinship,” so that we would hasten and compete to uphold those bonds. Otherwise, the decree is settled: a man is either destined to maintain his kin and receive that reward, or he is destined to neglect them and be deprived of it. The Prophet ﷺ informed us of this in order to spur us on to keep the ties of kinship.
Be aware that the writing in al-Lawḥ al-Maḥfūẓ (the Preserved Tablet) is followed by other kinds of writing. One of them occurs when the fetus in its mother’s womb reaches four months. Allah sends an angel entrusted with the wombs; the angel breathes the soul into the child and is commanded to record four matters: his provision, his lifespan, his deeds, and whether he will be wretched or happy. This inscription is different from the writing in the Preserved Tablet; it is written at the very outset of the person’s earthly life, which is why the scholars call it “the lifetime writing.”
There is yet another writing that takes place every year, on the Night of Decree (Laylat al-Qadr). On that night Allah decrees what will occur during the coming year, as He says: “Indeed, We sent it down on a blessed night—for We are ever warning—on that night every precise matter is made distinct” (Ad-Dukhān 44:3-4). The phrase “made distinct” means clarified and set forth in detail; hence the night is called the Night of Decree.