Is it permissible to divorce a woman and marry her sister while the divorced woman is still alive?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

There is no harm in marrying the sister of your divorced wife after her waiting period finishes. That is because the sister of your wife is temporarily forbidden for you, so if the reason is no longer existing- when her sister is still your wife-then she is not forbidden for you to marry her, after the waiting period finishes. 

Allaah Knows best.