Is it permissible to supplicate with the formula: "O Lord, grant my mother a long life in goodness and righteous deeds"? And is the benefit of the Prophetic tradition regarding maintaining kinship ties in prolonging life realized after a certain period of maintaining kinship ties, or by maintaining kinship ties through calls, or is a visit necessary?

It is permissible to supplicate for one's mother for a long life filled with goodness and righteous deeds, and this is a legitimate supplication. It has been established that maintaining kinship ties (silat al-rahim) increases one's lifespan, and scholars have discussed this increase in detail. We hope that Allah grants those who maintain their kinship ties, by whatever means possible for them—such as calling or sending greetings—the rewards He has ordained for maintaining kinship ties.