In the postbit template, find this and delete it:
HTML Code:
<if condition="$post['rank']"><div class="smallfont">$post[rank]</div></if>
And move it to here (in red):
Code:
<td nowrap="nowrap">
<if condition="$post['rank']"><div class="smallfont">$post[rank]</div></if>
<div id="postmenu_$post[postid]">
<if condition="$show['profile']">
<a class="bigusername" href="member.php?$session[sessionurl]u=$post[userid]">$post[musername]</a>
$post[onlinestatus]
<script type="text/javascript"> vbmenu_register("postmenu_$post[postid]", true); </script>
<else />
$post[musername]
</if>
</div>
That should put it below the avatar and above the username. If using the postbit_legacy template, do similar (the <td> tag is a bit different in the postbit_legacy, but the username stuff is all there).