Though, she is an ex employee but she is now with advance with her skills, knowledge and experience and also it is not necessary that the conditions of employment will remain the same for years.
You must treat her as your new employee and need to issue a new appointment letter, employee code and need to create a new file with her updated documents such as her present experience cum relieving letter (For the period she has spent with other employer then you till date), copy of updated CV, Contact and present communication and other statutory required docs.
And about appointment letter for this employee, as I told you above that she now must be treated like a new employee, you can use your present appointment letter format. An old/ex employee can get many internet/external benefits but there should be no lacks in following the procedure of hiring an employee.
About issuing her a new EPF/ESIC code/no, hope you are aware of the updates from the department. You can use her present EPF number with the employer as the transfer of it is also available. for more need to visit "Official EPF Portal"
in short : treat her as a new employee and complete the task.
In-House HR & IR Advisor