Praise be to Allah.
There is no sin on you if you do not invest this money, because you have only taken it to keep it as a trust. What you have to do is keep it safe, and give it to its owner when she asks for it, because Allaah says (interpretation of the meaning):
“Verily, Allaah commands that you should render back the trusts to those, to whom they are due”
And the Prophet (peace and blessings of Allaah be upon him) said: “Give the trust to the one who entrusted it to you.” Narrated by al-Tirmidhi (1264) and Abu Dawood (3534); classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
You should advise this sister and explain to her that this wealth is subject to zakaah, and tell her that zakaah may consume it if she does not invest it.
We refer to the hadeeth, “Whoever takes care of an orphan who has wealth, let him invest it in trade and not leave it to be consumed by zakaah.” This was narrated by al-Tirmidhi (641) and classed as da’eef by al-Albaani in Da’eef al-Tirmidhi, but its meaning is sound and clear, because the orphan’s wealth is like the wealth of any one else: if it reaches the minimum threshold (nisaab) and one full hijri year has passed, zakaah is due on it. If it is not invested, zakaah must be taken from it every year, which will lead to it decreasing.
This is proven in the words of ‘Umar (may Allaah be pleased with him): “Do trade with the orphan’s wealth so that it will not be consumed by zakaah.” Narrated by al-Daaraqutni and al-Bayhaqi, who said: Its isnaad is saheeh.
And Allaah knows best.