You can do it with the following script structure:
Enter Find Mode (no restore and pause)
Copy (select field you want to copy)
Perform Find (no restore)
The criteria that the user entered is now in your clipboard and you can store it numerous ways (ie go to another file, create record, paste value)
Note: To make this work you will have to assign the script to a button in your interface so that the user uses the script and not a FMP search.