Answer
Wa `alaykum as-Salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister, thank you for trusting us and for your question that shows your concern to be more knowledgeable about Islam and its teachings and rulings.
As for your question, the husband’s son from another wife is, with regard to inheritance, a stranger and has no inheritance share in this wife’s estate.
In his response to your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
If this married woman dies, as you said, she has no father, no child, she has a husband, a mother and a brother; distribution is derived from the verses 11 and 12 of Surat An-Nisaa’ (No. 4).
It is as follows: mother inherits 1/3 (a third) of her estate, the husband takes 1/2, and the brother takes the remainder 1/6. Her husband’s child does not inherit anything, as he is stranger to her.
Remember also that the child of the husband is, with regard to inheritance, a stranger to his step mother and to her mother as well.
Also once the daughter dies, her husband becomes, with regard to inheritance, a stranger to her mother.
If the mother dies before her daughter, she is inherited by her two children, male twice as much as female. If she dies after her daughter whatever she inherited from her daughter was hers and will be inherited by her own heirs, as in this case she is survived by her son; he is the only heir.
Allah Almighty knows best.