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Interests: Movies, always trying to get things better, Wasting money on things I don't need, reading stuff on here, eating sandwiches & being thankful for the small things
It looks as though it's just a normal frame with mountboard and then the canvas and inner frame on top of the mountboard.
You could just use the fillet and screw it in place from behind the mountboard. Another option would be a small l-shaped moulding, or even a normal moulding on its side or upside down, depends on the sizes needed and the depth of the canvas.