I am now working on another servlet which will also be using this method. I want to know the best way I can share it between both servlets. I was thinking of creating a final class and make the method a static method. Is this a good way of dealing with this issue ?
You should move that part (only, code which can be reused and not the things usually go in servlets like setting the content type etc.. ) in to a separate class and let the servlets (or other components) call it, in that way any changes for that can be made easily later.