1. There was provision to relieve employee in the employment letter, with or without pay
2. The employee was not deprived of his right to compensation for the notice due to a non-compliance of your company policies
In your case it is evident that -
1. the employee resigned on his own and agreed to serve three month notice period
2. salary for month 1 was paid to him for the time he worked for your company
3. salary for month 2 is still not paid
4. salary for month 2 can be set off against the last month notice 'which the employee is not intending to serve'
It is important that condition, as I outlined in clause 4 above was agreed to with the employee and substantiated by a prima-facie evidence. If it was agreed then you are all set to set off of month 2 payable with month 3 notice. If there was no agreement, please release month 2 salary and move ahead with the recovery proceedings for notice period not served, i.e., month 3.
What is your Company HR Policy says?. Is the terms of employment speak about this? If so, you can recover balance NP amount from the final settlement or dues payable to the employee.