Sharing a link from a Facebook post using the iOS app may not be all that obvious, but the feature does exist.
To share a link you'll need to be viewing the post from your News Feed. Tap on the link to open it. Next, tap on the action (or share) icon at the top of the screen. You will then be presented with three options, one of which is the ability to share the post.
It's important to note that you have to access the post from your News Feed. If you're to navigate to the wall of the Page you'd like to share the post from, the share option is mysteriously no longer present. The video below will walk you through the sharing process.
Oddly enough, the same feature is completely missing from the Android app. When tapping on the link, your default browser is opened, taking you out of the Facebook app altogether.
How do you normally share a post or link with Facebook while mobile?