The process of termination in such cases takes strength from the employment form itself, where it is normally written that the information provided hereinabove for seeking employment is true and nothing has been hidden in the organizational interest.
In view of this, a paragraph is added in the appointment letter for the punitive action of hiding such information, which warrants termination. Invariably, cases are on account of stating higher qualifications or higher salary. In such cases, some companies have taken a lenient view and consequently adjust the salary of the employee if the position is critical or demote the candidate equal to his qualification or salary (This saves a lot of time and cost of recruitment and, in turn, the company gains the trust level of the candidate). Largely, people have been asked to leave, considering substantial evidence after verification and company policy.
Therefore, the recommendation for issuing a relieving letter is against tendering resignation and not termination. The principle of discharge simpliciter applies in such cases, where no inquiry is required, and you can terminate the employee post-facto if the employee resists resigning.
Please avoid issuing a letter of appointment until you complete your verification process if it is mandatory for all positions.
As a good HR practice, companies nowadays get the verification done before the joining of the candidate, and they use a third party for such services, which are faster, and the company avoids taking the candidate on the roll rather than terminating after appointing.
This is a process that indirectly disturbs your attrition ratio. Think of HR as a business partner; a delayed process of verification directly impacts the business.
I think the suggestions given above are valid and go with what best fits the situation.
Parashar