Possible with custom coding - intercept and inserts variable as a get parameter via url to second page which reads parameter and inserts into field.
#Here are the tools you need to put above script together
Submit to second page:
Simply change form action to second page’s relative URL.
Get parameter from URL:
How to get URL parameter using jQuery or plain JavaScript? - Stack Overflow or url - How can I get query string values in JavaScript? - Stack Overflow
Get an element on the page:
https://learn.jquery.com/using-jquery-core/faq/how-do-i-select-an-item-using-class-or-id/
Set value of a form field: