Can Employer reverse the termination letter? What is the actual procedure in this case?

Hey Y'all, Hope you all are doing great. I have a confusion which I need to clear. Actually I have sent the termination email to an employee with the attachment of termination letter. The employee doesn't want the tag of termination on his career. Now we have an other option that is of the normal resignation and I have no issues with proceeding normal resignation.
My question here is Should I email him first mentioning that your termination has been reversed or should he email me with the resignation email asking to consider it as a normal resignation and remove the tag of termination?
Please answer as per the study and HR practice. What is the actual procedure in this case?

considering the future carrier, it is better accept his resignation first and with draw the termination letter issued to him. Issue him simple relieving letter based on his resignation letter, with a waiver of notice period if any, required under terms and conditions of employment.

Alright. So according to you he should first send me the resignation email requesting to accept that. Right?
Then I will proceed with further procedure.

Hi,
Please collect a request letter/email from the employee about the receipt of termination letter and also requesting the Management to accept apology and to relieve him/her properly.
To safeguard your organization the above letter with reference about termination is advisable. However in cause of any future verification for the said employee, reason for relieving can be presented as Resignation. Termination reversal is internal and for file purpose.

Management can consider resignation in lieu of termination, provided the case is not a severe kind of misconduct. The mangaement forefit the gratuity & bonus payble to employee on termination of service than of resignation.
You verify the case at your end if there is no such financial implication is existing, then call the person take his resignation letter and other written signed paper as you feel the right for the case to avoid future complecation.

Termination is provided due to the severe gravity of offense refer to the company code of conduct and any financial goodwill may be forfeited or when an employee has reach end of the contract.
Resignation normally coming from an employee when deciding no longer want to be in service with the company.
Advise to resign is coming from the company decorum/HR for some reason to protect somebody's integrity and this is an internal or discrete measure.