How do I share a post in the Facebook app for iPad?
You cannot re-share posts from the iOS Facebook app. 

You can re-share posts if you:


Browser to https://www.facebook.com/ in mobile Safari
Log in
Click the three bar icon in the upper left hand corner to bring up the side bar  
Scroll to the very bottom of the side bar
Click the "Desktop Version" link at the very bottom of the side


This will give you the full Facebook desktop web view and from here you can re-share posts in your timeline.