If you have relieved the employee on May 31st, the date of exit should be 31st May. At the same time, if you have paid salary till 8th July, then PF should also have been deducted, right? Then the date of exit should be July 8th. Now if you have settled the dues as of 31st May but have paid 'compensation' or notice pay for early relieving, then you should account that part of the salary, i.e., salary for the month of June and July till 8th, as Notice Pay and not as Salary. Then you need not deduct PF in June and July, and you can exit the employee on 31st May itself. If the employee joins a new company before July 8th, it will not clash with the joining date in his new company. I recommend that you should mark the exit on May 31st itself and whatever amount is payable for the period from 1st June till 8th July should be paid as compensation for early relieving or Notice Pay, which will not attract PF.