How to re-attach toilet paper holder post back onto wall
In your photo of the "post" you can see a screw (called a "grub screw" in the UK or a "set screw" in the US, if you want the terminology). You need a small screwdriver to loosen off this screw. The post will then fit back over the wall bracket, and you tighten up the grub screw to reconnect the post to the wall.