To reproduce (using Internet Explorer 11):

1. View topic with replies
2. Click Post Reply button
3. In Topic Review section click on quote button of a reply with new lines

The result is that you end up with text such as:

[quote="DavidIQ"]This is a post.<br abp="374"><br abp="375">This is a link:  http://www.phpbb.com/community/index.php<br abp="376"><br abp="377">[b]This is some bold text.[/b][/quote]

Chrome does not seem to have this issue.