hi ,you need custom search engine for the forum here you can build
https://www.google.com/cseonce filled the Forum and other data, press the Create
next screen, congratulate us, and click get code
copy that piece of code:
when you have this piece of the search engine, adds that ID in this JS
Code:
  $(function () {
  //Here's LINE CODE SAVED PREVIOUS STEP
  var cx = '0034546779763163:h_rtrtj_qrt';
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  if($("div#search-box").length){
  //phpBB3 with search
  $("div#search-box").html("<div id='my_gs'><gcse:search></gcse:search></div>");
  }else{
  if($("div#page-body").length){
  //phpbb2, phpBB3 no search engine and punBB
  $("<div id='my_gs'><gcse:search></gcse:search></div>").insertBefore("div#page-body");
  }else{
  //Invision
  $("<div id='my_gs'><gcse:search></gcse:search></div>").insertAfter("div#submenu");
  }
  }
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  var gcse = document.createElement('script');
  gcse.type = 'text/javascript';
  gcse.async = true;
  gcse.src = (document.location.protocol == 'https:' ? 'https:' : 'http:') +
  'http://www.google.com/cse/cse.js?cx=' + cx;
  var s = document.getElementsByTagName('script')[0];
  s.parentNode.insertBefore(gcse, s);
  });
Positions in all pages,Try it in our forum works great
search the forum for any word that contains the topic or title