Yep.
$_SESSION['query2'] = $query1;
//although the way you have it is fine, this is much cleaner
echo "Session is ".$_SESSION['query2'];
//you can use the double quotes, but unless you need the preprocessor
//to interpet the string first, it is best to use single quotes
echo '<input type="text" name="query1" value="'.$_SESSION['query2'].'" size="'.$qsize.'" readonly />';
//or like you had it, only fixed
echo "<input type=\"text\" name=\"query1\" value=\"{$_SESSION['query2']}\" size=\"$qsize\" readonly />";
You were missing the type and you forgot to enclose the properties values with double quotes. I suppose you don't HAVE to enclose them in double quotes if there are no spaces in the value, but personally, those 2 extra keystrokes can save you a lot of hassles with broken code and standards compliance.