<?php
$re = '/(")([^"]+)(")/';
$str = 'The nice man said "How\'s things today" and I replied "All is good thanks".';
$subst = '<i class="fa fa-quote-left" aria-hidden="true"></i>\\2<i class="fa fa-quote-right" aria-hidden="true"></i>';
echo preg_replace($re, $subst, $str);
The nice man said <i class="fa fa-quote-left" aria-hidden="true"></i>How's things today<i class="fa fa-quote-right" aria-hidden="true"></i> and I replied <i class="fa fa-quote-left" aria-hidden="true"></i>All is good thanks<i class="fa fa-quote-right" aria-hidden="true"></i>.