I have been thru this process, Its simple, you should meet all the cretira in the LC which you will be using, like Qualifications should be equal or may be more as mentioned in the LC which was approved for person X, you skill set should match with that, you current salary.
Lawyer will Apply for substitution on your behalf while filing I-140 and then I-140 will be approved in your name.
Hope this helps.
Thanks