Is it permissible for children to search for their deceased mother's father, whom she never knew?

The Sharia (definition) commanded the upholding of kinship ties and urged the knowledge of lineage through which these ties are maintained, based on the hadith (definition): "Learn enough of your lineages to uphold your ties of kinship, for indeed, upholding kinship ties increases love among family, multiplies wealth, and prolongs life." Knowledge of lineage is obligatory to avoid marrying maharim (unmarriageable kin) and to identify those entitled to inheritance. Therefore, it is obligatory to know one's grandfather, paternal uncles, paternal aunts, and their children if possible. Otherwise, there is no sin, as Allah Almighty says: "Allah does not burden a soul beyond its capacity."