Genetic Genealogy Tips & Techniques is a Closed Group on Facebook. According to the Help Center's FAQ What are the privacy settings for groups?, only current members of a group can see the content of the group, even when it is shared outside the group.
I admin some closed groups on Facebook. The context is a mix of news items and personal postings. For ordinary news items, I might share those in the groups and on Twitter -- but for the personal postings, there is an expectation that the information doesn't go beyond the group. That was the whole point of making the groups closed -- that the members' participation won't be broadcast in their News Feed on Facebook.
The National Genealogical Society offers some guidelines as a PDF download: Guidelines for Sharing Information With Others Recommended By the National Genealogical Society. They suggest that
genealogists and family historians respect the restrictions on sharing information that arise from the rights of another as an author, originator, or compiler; as a living private person; or a as party to a mutual agreement
If something wasn't meant to be widely shared on Facebook, then it seems reasonable to assume that it shouldn't be shared outside Facebook either.
I would say that only options three and four -- posting the question with the permission of the original poster, or inviting them to post here so you can share your answer, are acceptable.
Whatever you decide to do, I would recommend making a copy of the question and answer for your personal archive.