Changing the module weight will work, but sometimes that can cause problems with the order in which other hooks in your module are invoked.
Drupal provides hook_module_implements_alter() for exactly this sort of situation, so that you can target the order a specific hook is run in:
Alter the registry of modules implementing a hook.
This hook is invoked during module_implements(). A module may implement this hook in order to reorder the implementing modules, which are otherwise ordered by the module's system weight.
The code might look something like
function MYMODULE_module_implements_alter(&$implementations, $hook) {
if ($hook == 'form_alter') {
// Move MYMODULE to the end of the list.
$group = $implementations['MYMODULE'];
unset($implementations['MYMODULE']);
$implementations['MYMODULE'] = $group;
}
}
Once you clear the cache your module's implementation of hook_form_alter() will be invoked last (unless of course another module is implementing hook_module_implements_alter() and altering the order again. But that's a different story).
I personally prefer this method as it's just a simple code change, no need to maintain any changes to the system table in the database.
I'm not sure how well that works with a form_FORM_ID_alter hook (never tried it), but with this method you can at least make sure that only the weight for hook_form_alter() need be updated.
Actually looking at the code for drupal_alter(), changing the conditional to if ($hook == 'form_search_form_alter') would probably work.
