Need to copy the text inside an <a> tag and move it inside a specific <div>

Answer 1

You probably want to use .text():

$('#sideNavHeader').text($('li.selected a').text());

Answer 2

Tobias Cohen's selector was much better than mine you should use:

$('#sideNavHeader').html($('li.selected a').html());

instead of my original code:

$('#sideNavHeader').html($('li.selected').children('a').html());