There is a difference between linking a photo and copying it and republishing it. Linking to it is not a problem. If you copied it and republished it, even though her settings on FB are 'public', there is still an owner to the photo. It may not even be the FB page owner. However, prior to any action for copyright infringement the owner would need to request you take it down. This is often referred to as a DMCA take down notice. Once that request is made, if you refuse to take it down, then 'yes' there could be potential liability. Just because a person posts a photo online and doesn't put the copyright symbol next to it does not mean there is not an owner that has rights to protect. So, be careful in copying any photos online and republishing them. If you receive a DMCA take down notice, it is usually best to comply, unless there is some overwhelming reason not to, such as 'you actually own the photo', 'you know this entity does not own the photo', etc.
The recommendations in this answer are not considered legal advice for the purposes of ethical evaluation, nor do the create a retention of counsel wherein an attorney-client relationship exists. These recommendations should never be relied upon without first consulting an attorney in your jurisdiction. I am not your attorney, unless we enter into a written agreement fulfilling the terms of that agreement. The comments posted herein are purely for educational purposes and public discourse only.
You say you posted the photograph via a link so let's put aside the non-issue of you copying and then publishing the other person's photograph on the forum.
There are two kinds of links:
(1) A "normal" hypertext link that appears on a webpage as simply some other web address or other alphanumeric string that, when clicked, instructs a browser to retrieve the linked-to webpage by either opening a new browser window to view it or by viewing it within the same browser window as the one used to click on the link. Publishing a normal link on a webpage that re-directs the viewer to a publicly available webpage is not unlawful -- and is, in fact, the entire premise of the internet.
(2) An "in-line" hypertext link "allows one to import a graphic from a source website and incorporate it in one's own website, creating the appearance that the in-lined graphic is a seamless part of the second web page. The in-line link instructs the user's browser to retrieve the linked-to image from the source website and display it on the user's screen, but does so without leaving the linking document. Thus, the linking party can incorporate the linked image into its own content." Kelly v. Arriba Soft Corp., 336 F. 3d 811, 816 (9th Cir.2003). Publishing an in-line link -- the end result being that the linked-to image is displayed on the linking webpage as well as the webpage where it was originally published by its owner -- is NOT, at least in the 9th Circuit, a direct infringement of the copyright in the photograph. See Perfect 10, Inc. v. Amazon. com, Inc., 508 F. 3d 1146, 1161 (9th Cir.2007). However, if the owner of the copyright in the image can prove that someone visited the linking webpage and copied the image without a license then the person who posted the in-line link may [just may] be liable for contributory copyright infringement. In-line linking is ubiquitous on the internet and I have NEVER heard of contributory copyright infringement liability being found based on an in-line link.
In short, linking to publicly viewable websites is lawful [so long as the linked-to content is lawful for everyone to view -- that is, nothing obscene, no trade secrets, nothing classified, etc.].
But ... if the content before and/or after the link disparages the person whose image is linked to or somehow invades that person's privacy then the link -- along with the rest of the information about the person -- would be unlawful.
See your own attorney about this matter.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
I cannot see how a link to a public image is a cause for action assuming, as my colleague notes, you did not add some defamatory note to the link, like "child molestor" has your hotlink
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