Using the Facebook app... hit the Share link... then 'write post'... then at the bottom, tap "on your own timeline" to select where the post will go.
Right next to "To:" it should say "Friends", click on Friends and it will allow you to should allow you to choose who it is shared with (including groups).
There has been a lot of updates to the FB App lately have you tried it in Safari
Sent from my iPhone 5s Gold 64GB
Only the mobile fb comes up in safari, it works the same. Can't so it.
Would have to go on chrome browser and use the desktop site for Facebook to be able to share it to a group
~ Sent from my Sexy iPhone 5s Gold on Tapatalk ~