Setting POST variable without using form

Yes, simply set it to another value:

$_POST['text'] = 'another value';

This will override the previous value corresponding to text key of the array. The $_POST is superglobal associative array and you can change the values like a normal PHP array.

Caution: This change is only visible within the same PHP execution scope. Once the execution is complete and the page has loaded, the $_POST array is cleared. A new form submission will generate a new $_POST array.

If you want to persist the value across form submissions, you will need to put it in the form as an input tag's value attribute or retrieve it from a data store.

If you want to set $_POST['text'] to another value, why not use:

$_POST['text'] = $var;

on next.php?