When the withdrawal forms are submitted by the company officials at the PF department, they provide an acknowledgment receipt. An acknowledgment receipt confirms that the PF withdrawal forms (Form 19, 10C, 3A) for the employee named "so and so" have been submitted on a specific date.
You can ask your manager to give you a copy of that acknowledgment receipt. Based on that, you can go to the PF Department yourself and check the status.
Once the receipt is received by the company, they typically do not follow up as their task is considered complete. If you are concerned about your money, you can take responsibility, but it may be unclear whose responsibility it is. However, you have already mentioned that you are not worried about the money, so the matter ends here.
Regarding Your Simple Question
It is (but not) the company's obligation.
Regards,
Hiral