The short answer is probably "No." There was no "invasion" of your privacy. You put your post out there for all your friends to see. The only thing this person is guilty of is being a terrible friend.
This answer is provided for informational purposes only, is based upon the limited facts provided by you, which are assumed to be true and accurate. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
You consented to review of your postings by your friend. However, your friend had no right to make a copy of your posting and provide it to your supervisor. In so doing, your friend may have technically engaged in copyright infringement----but you can't bring a copyright infringement claim unless you registered your original work with the copyright office. Since I doubt that you registered your Facebook posting, you probably can't sue your friend for copyright infringement. You might also be able to sue your friend for intentional interference with contractual relations if you can show that he intended to harm your employment relationship by providing the photograph to your supervisor. In truth, however, when you decided to put your posting on Facebook, you gave up most of your privacy rights in the posting and it will be hard for you to do much about this (other than "unfriend" this friend).
I don't think you have much of a case unless your FB friend specifically signed a non disclosure agreement with you.
This is not legal advice but a general comment on society based on a limited set of hypothetical circumstances. No one should act or refrain from acting based on these comments without seeking appropriately licensed legal or professional advice. The author disclaims all liability in respect to actions taken or not taken based on his comments.