Is it permissible for the sister of a deceased to perform hajj on her behalf wherein the latter's son covers the expenses? 

Please note that the deceased did not leave any money, her son has not yet performed his own [obligatory] hajj, and that her sister had already done so.

If the case is as mentioned in the question i.e. that the deceased's sister has fulfilled the obligation of hajj, then there is no legal impediment to performing it once again on behalf of her sister, even if the money is donated by the son of the deceased (as long as he willingly gives it for this purpose). This is not incompatible with the fact that the son has not yet performed this duty.

The above answers the question and Allah Almighty knows best.