Is it permissible for a sister's husband to give from his Zakat money to his virgin wife's sister who lives in his house, knowing that her parents are far away and their circumstances are difficult?

There is no objection to giving a wife's sister from zakat (definition) if she is poor and has no provider. Zakat for her is better than for others because it is both charity (sadaqah (definition)) and maintaining family ties (silah). It must be noted that her sister's husband is not a mahram (definition) to her, so it is not permissible for her to uncover before him or to be in seclusion with him.