rosegarden,
I can not see the header.inc file - however unless that file has $GET[] and $POST[] variables in it, you are correct.
If the information is being posted, use $variable = $POST['form_varname']; and likewise, if you are using the GET method, you can use $variable = $POST['frorm_varname'];
You can both use it inline:
<INPUT type=\"text\" name=\"sender_phone\"
value=\"{$_POST['sender_phone']}\" size=30></p>
Which I would not recommend doing so with any SQL query as it leaves you completely open to SQL Injection attacks.
You can declair all of the used variables in the head of your document with the $variable = $_POST['form_variable']; and the remainder of your code should then work.
Good luck!