The state cabinet, which met under the chairmanship of Chief Minister Parkash Singh Badal, cleared the appointment of Swapandeep Kaur.
An official spokesperson said that Sarabjit had succumbed to a attack in Lahore jail and subsequently the state government had declared him a martyr.
Besides sister Dalbir Kaur, Sarabjit is survived by his wife and another daughter.
Sarabjit, 49, had sustained severe injuries after at least six prisoners attacked him in a barrack at Kot Lakhpat Jail Lahore.
He died on May 2.
Meanwhile, the Cabinet also cleared appointment of Manjit Kaur. 11 members of Kaur's family were killed in a road accident near Moga on May 6, 2012.