Depending on how the funeral home is using your late mother's obituary (e.g., as an advertisement or merely as an example of its past work), you may or may not have grounds for initiating legal action. Keep in mind that if the obituary was publicly available on one or more websites, it is generally within the public domain (at least the pertinent information contained therein), and therefore, generally not subject to some type of copyright. If you believe there is a sufficient basis for which to seek the removal of it from that Facebook page, you may want to hire an attorney to draft a cease and desist letter, but other than that, there is likely nothing more that could be done, absent a showing that you and/or your family has/have actually suffered some type of cognizable damages beyond simply being annoyed or somewhat distressed. Good luck.
It's tacky and descicable, but probably not illegal.
Contact Facebook. They may remove it. Also call your local newspaper and TV station's consumer reporters. I suspect they'll jump on this. The negative publicity for this sleazy funeral director may pressure him.
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