Yes, the employee has to confirm the cancellation of his resignation either in a separate letter or in the same resignation letter in his own handwriting. Later, an increment letter can be issued. You may include an increment reversal clause in the increment letter, stating that "in the case of resignation within 2 or 3 months from the effective date of the increment (as per your company norms), the increment will be reversed." The reason is that many employees have lately used this as a technique to bargain for an increment with their current employer and then negotiate with a new employer immediately to gain more monetary benefits within a short period of time.
Also, advise the concerned employee to keep this information confidential, as otherwise, you may receive more resignations from others.
Thank you.