There are two queries in this thread. One is about final settlement and the other is about PF transfer or settlement. Let me address PF first and then Final settlement.
1. PF Settlement
It is a procedural requirement that an employee needs to forward their application through their old employer. If they do not forward it in a reasonable period, say 7 to 10 days, send a letter to them and mark a copy to the PF Commissioner. You will get addresses from the website. If they still do not send it within the next 7 days, lodge a complaint with the PF Commissioner. Keep all copies with you. If there is no action for another 15 days, send another reminder to the Regional Commissioner. If there is no response within 15 days, send a complaint to the Central PF Commissioner. The entire process should be completed within 60 days. I have personally seen this working in many cases. I have received communication from both the Regional and Central Commissioners. If an employer does not respond, an Inspector comes for an inspection.
2. Final Settlement
There is no law that says the settlement shall be made within 45 days. At least I am not aware of any. But gratuity shall be settled within 30 days. In the case of termination, settlement shall be made within two days. Wages for a particular period shall be made within 10 days of the closure of attendance. Hence, one can reasonably presume that a delay beyond thirty days is unreasonable.
Some companies have the practice of insisting on a "No Due Certificate." Please insist on this certificate if there is no such practice. This must be given by the employer on the day they get relieved. If you have a certificate with no dues, your balance will have to be settled immediately. If they do not settle, then send a letter to the CEO and request their intervention. If you do not get a response, then lodge a complaint with the Payment of Wages Authority. This is normally the Assistant Commissioner or Deputy Commissioner of Labour of your region. You may assign this job to an advocate who normally charges between 10% and 20% as fees. I am aware that many times this delay is caused due to a lack of urgency. Lack of coordination between HR and Accounts is also a reason. In some cases, the operational Head would have stopped this with Accounts and they do not give clearance certificates easily.
In short, get a No Due Certificate before getting relieved, wait for a month, then send a reminder to the CEO, wait for a week, then lodge a complaint with the Payment of Wages Authority. This will generate pressure for the employer to close the issue faster.