Praise be to Allah.
There is no sin on your sister if she gives you money as a loan for you to invest and benefit from the results on the basis that the capital will remain your sister’s. But if your sister wants to share the profit with you whilst she is keeping the capital as is, that is not permitted, because this comes under the heading of “every loan that brings benefits is riba.” It is not necessary for her husband to know about your giving her the money, because the money is her own and he has no right to any part of it unless she gives it willingly. Allaah says (interpretation of the meaning):
“And give to the women (whom you marry) their Mahr (obligatory bridal-money given by the husband to his wife at the time of marriage) with a good heart; but if they, of their own good pleasure, remit any part of it to you, take it, and enjoy it without fear of any harm (as Allaah has made it lawful)”
But by way of kind treatment and because men are more experienced and kanowledgeable in matters of business, our advice is that the husband should be told about what his wife is doing and how she is disposing of her wealth.
Shaykh ‘Abd-Allaah al-Jibreen said:
The wife owns her wealth and she has the right to dispose of it. She may give it as gifts, give it in charity, pay off her debts, give up her rights to money that she is owed or give up her right to inheritance to whomever she wants, whether relatives or others. Her husband has no right to object if she is mature and of sound mind. Her husband does not have the right to dispose of any of her wealth except with her consent. (Fataawa al-Mar’ah al-Muslimah, 2/674).
And Allaah knows best.