使用来自私人网站的phpmailer的链接嵌入图像是收件人无法看到的

Using phpmailer I need to build an email with an embedded image which has a link.
At the body of the message it is trivial to include

<a href="link"><img src="URL of the image to embed" /></a>

My problem is that that URL is protected by username and password so the recipient of the email cannot see the image, just a broken thumbnail with the link.
I tried using file_get_contents() as I read in other questions but didn't get the solution.