brons.dev,
 сделайте макет 
<!doctype html>
<html lang="en">
<head>
  <meta charset="utf-8">
  <title>autocomplete demo</title>
  <link rel="stylesheet" href="http://code.jquery.com/ui/1.10.4/themes/smoothness/jquery-ui.css">
  <script src="http://code.jquery.com/jquery-1.10.2.js"></script>
  <script src="http://code.jquery.com/ui/1.10.4/jquery-ui.js"></script>
  <script>
$(function () {
             $("#go").on("click", function () {
                 $("#autocomplete").val("j")
                 $("#autocomplete").autocomplete("search" , $("#autocomplete").val())
             })
             $("#autocomplete").autocomplete({
                 source: ["c++", "java", "php", "coldfusion", "javascript", "asp", "ruby"]
             });
         })
  </script>
</head>
<body>
<label for="autocomplete">Select a programming language: </label>
<input id="autocomplete" >
<input id="go" name="" type="button" value="буква j" >
</body>
</html>