How can I post status with picture to Facebook Pages? (it is community page and posts are under page identity)
I've tried with native WP8 FB support, IE browser, and MS dedicated FB app, but there is not option for picture upload?
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So I suggest you take a look at FB Pages Manager:
The app allows you to post, delete or share your pages status, upload photos, send and receive messages from your pages, comment on your posts or reply to a comment. You can view all your page insights, like or unlike. Basically you can do pretty much everything on your pages that you do on your PC browser.
Pin your pages to your start screen and get notifications even when the app isn't open.
You can use your phone theme or the Facebook theme in the app.
I had found two versions, one paid and another free but didn't check them:
I'm not affiliated with the developers of that app and I'm not responsible for the information quoted above from WPCentral. Try the apps before buy.