Here's some custom content that'll do what you need:

<script>
$(function() {
  let f1 = $('#Button_Filter').closest('table');
  f1.prependTo(f1.parent());
});
</script>

Where might you place this? 

Within Administration -> Customisations you would edit the actual Filter Box you want to affect (or switch Inline Customisation on and get to the screen definition that way) and put the code (including the <script> tags) into the 'Custom Content' field.

That said, the code is *probably* specific enough that you could apply it more pervasively - by creating a .js file (called anything at all) in your WWWRoot/js/custom folder and putting the code in there (minus the tags in this case). Once you restart the CRM App Pool then the code will be applied to all of the list filters.

Within Administration -> Customisations you would edit the actual Filter Box you want to affect (or switch Inline Customisation on and get to the screen definition that way) and put the code (including the <script> tags) into the 'Custom Content' field.

That said, the code is *probably* specific enough that you could apply it more pervasively - by creating a .js file (called anything at all) in your WWWRoot/js/custom folder and putting the code in there (minus the tags in this case). Once you restart the CRM App Pool then the code will be applied to all of the list filters.

Perfect exactly what I wanted.  Thank you for your time.