To get the form contents to transfer you will need to apply the behavior for set form from cookie on part two. In order for this to work you must ensure that the two forms have elements named the same. If the form element names do not match the values will not be populated.
I did this in an example by applying the store form in cookie behavior to the first form. Then on the second form I added a checkbox. With the checkbox selected I added the set form from cookie behavior. When the box is checked it will set the value from the cookie to the corresponding form elements in the new form. I'm including an example of this for reference.