How do I pass a string from a PHP field to the PHP filter?
You can copy the code from the php field and add some logic to it to return false or true depending on the result but no there is no current way to transfer it.

EDIT: This may seem a bit backwards, though if you made a $_SESSION variable as an Array() you could maybe do something with that. Maybe not very helpful. views_php has always been entirely buggy for me and it comes in handy sparingly.