You basically need to change your code on A.php to
<form action='B.php' method='POST'>
<input name="text1" type="text" id="text1" value="default" />
then on B.php you will have your form:
<form action='C.php' method='POST'>
With any new input fields and hidden fields:
<input name="text1_b" type="hidden" id="text1_b" value="<? echo $text1; ?>" />
the:
<? echo $text1; ?>
carries the text from the input on A.php through to B then C.php