send photos from my email to a facebook user with no email?

Don't send them from your email. Use your FB acct and access your image files there.

FB has a Messenger application within it. Just msg them on FB and attach the photo to the msg. they should be able to download the image from FB messenger but just make sure it's not a super large sized file.

I wasn't aware that you could be a member of FB without having an email account. How is that even possible? Something sounds fishy or info is missing from this story.