Save field inputs upon submission of front end form for reuse in new form?
I don't know if we can compare the problem I usually have but here is my way.

Whenever I build a website where users can login and save "entries" they also need to stay connected to it off course.
I make sure the title of the new made entry got the users ID in it. So if someone makes a new entry they go to a succes page after the form is submitted. This success page is actually the entry they created. The moment they land on that page the "second" form will be automatically filled in with the details I need and then save/update whatever needs to be updated (most of the times for me that would be saving the entry to a user profile). After the second form submit's I redirect them to the page I want.

This would include some javascript.