Full And Final Settlement Of Employee

Problem - I have one employee who has submitted the resignation without notice. Unfortunately, his offer letter doesn’t mention him serving a notice period. This was my error.
However, the same was conveyed verbally to them at time of appointment.
Question – Am I obliged to pay him his entire compensation or can I have him serve notice/ take 1 month salary compensation?
Problem - Also, there is a company policy of a 45-day full and final settlement window which is not documented or communicated to the employees. Only after they resign do I tell them about this window.
Question - Am I sufficiently empowered to do so or do I have to convey it to my employees in writing?

""However, the same was conveyed verbally to them at time of appointment. ""
Verbal information has no real legal value if it gets contested or denied.
Make an exception in this case and get the employee cleared.
Do inform your senior management about the lapse and clear the matter.
FNF has to be done so point delaying an inevitable commitment.

If the Standing Order is not in place and accissable to the employees and the clause is not mentioned in the letter, then you will have to clear the employee dues with no Notice Period.
Having a policy and the employees not knowing it, or having no access to it, will not help you in enforcing the same.
The Standing Orders also need to be communicated and need to be available for the employee for ready reference.
Regards,
Ashutosh Thakre

Dear Paresh,
Informal or uncommunicated information pertaining to employer's police or employee's service has no relevance in the eyes of the law. So, neither your verbal information about notice period, nor uncommunicated information about the settlement window proposed to be communicated to the employee after his resignation has no relevance now.
However, you can follow and insist the employee on following the requirement of notice period, as prescribed in your state's establishment and commercial organisations Act.
For future, you may include the necessary clauses in the appointment orders of the newly appointed employees. POLICY DOCUMENT OF THE COMPANY SHOULD NEVER BE INCOMPLETE OR DEFECTIVE.

Please find the remarks as per your query in BOLD
Legally the salary has to be paid/cleared within 7 days of the month completed/last working day. The FnF apart from salary has to be paid within 30 days from the last working day.

Dear Paresh,
Nathrao has suggested the right thing. Just do a "JDI / Mini-kaizen" and correct similar goof-up's, if any so that you can work peacefully. Such kind of issues creates lot of confusion and can become a pain for HR if not tackled properly. So, clear it off as an "exception" after taking your management's approval.
The question of standing orders comes into play only if your set-up is a factory and where you do not have any other formalized agreement signed-off with the associates.
Cheers,
A.B.